\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand*\HyPL@Entry[1]{}
\citation{GrzymkowskiWitula}
\citation{Ireland}
\citation{Shevelev}
\citation{surowski}
\citation{Watkins}
\HyPL@Entry{0<</S/D>>}
\citation{wsw1}
\citation{wsw1}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{2}{section.1}}
\newlabel{roz1}{{1}{2}{Introduction}{section.1}{}}
\newlabel{w1-a}{{1.1}{2}{Introduction}{equation.1.1}{}}
\newlabel{w1-b}{{1.2}{2}{Introduction}{equation.1.2}{}}
\newlabel{w1-c}{{1.3}{2}{Introduction}{equation.1.3}{}}
\newlabel{w1-d}{{1.4}{2}{Introduction}{equation.1.4}{}}
\newlabel{w1-e}{{1.5}{2}{Introduction}{equation.1.5}{}}
\newlabel{w1-f}{{1.6}{2}{Introduction}{equation.1.6}{}}
\newlabel{w1-g}{{1.7}{2}{Introduction}{equation.1.7}{}}
\newlabel{w-and}{{1.9}{2}{Introduction}{equation.1.9}{}}
\newlabel{w-bnd}{{1.10}{2}{Introduction}{equation.1.10}{}}
\citation{wsw1}
\@writefile{toc}{\contentsline {section}{\numberline {2}Basic decompositions}{3}{section.2}}
\newlabel{roz2a}{{2}{3}{Basic decompositions}{section.2}{}}
\newlabel{wzor-gw1new}{{2.1}{3}{Basic decompositions}{equation.2.1}{}}
\newlabel{w1.10}{{2.2}{3}{Basic decompositions}{equation.2.2}{}}
\newlabel{wiel-114}{{2.3}{3}{Basic decompositions}{equation.2.3}{}}
\newlabel{wz116}{{2.5}{3}{Basic decompositions}{equation.2.5}{}}
\newlabel{w1.19}{{2.7}{3}{Basic decompositions}{equation.2.7}{}}
\citation{Yaglom}
\citation{ShklyarskyUSA}
\citation{ShklyarskyMir}
\newlabel{w2.8}{{2.8}{4}{Basic decompositions}{equation.2.8}{}}
\newlabel{lem2.1}{{2.1}{4}{Basic decompositions}{theorem.2.1}{}}
\newlabel{choinka}{{2.11}{4}{Basic decompositions}{equation.2.11}{}}
\newlabel{example2.2}{{2.2}{4}{Basic decompositions}{theorem.2.2}{}}
\newlabel{ex-w5}{{2.12}{4}{Basic decompositions}{equation.2.12}{}}
\citation{wsw1}
\citation{Shevelev}
\@writefile{toc}{\contentsline {section}{\numberline {3}The first group of special cases of\nobreakspace  {}(\ref  {choinka})}{6}{section.3}}
\newlabel{w2.1}{{3.1}{6}{The first group of special cases of~(\ref {choinka})}{equation.3.1}{}}
\newlabel{w2.2}{{3.2}{6}{The first group of special cases of~(\ref {choinka})}{equation.3.2}{}}
\newlabel{w2.3}{{3.3}{6}{The first group of special cases of~(\ref {choinka})}{equation.3.3}{}}
\newlabel{f2s-lem1}{{3.1}{6}{The first group of special cases of~(\ref {choinka})}{theorem.3.1}{}}
\newlabel{f2s-w1g}{{3.4}{6}{The first group of special cases of~(\ref {choinka})}{equation.3.4}{}}
\newlabel{f2s-w2g}{{3.5}{6}{The first group of special cases of~(\ref {choinka})}{equation.3.5}{}}
\newlabel{f2s-lem2}{{3.2}{6}{The first group of special cases of~(\ref {choinka})}{theorem.3.2}{}}
\newlabel{w2.11a}{{3.9}{7}{The first group of special cases of~(\ref {choinka})}{equation.3.9}{}}
\newlabel{w2.11b}{{3.10}{7}{The first group of special cases of~(\ref {choinka})}{equation.3.10}{}}
\newlabel{w2.11}{{3.11}{7}{The first group of special cases of~(\ref {choinka})}{equation.3.11}{}}
\newlabel{f2s-lem3}{{3.4}{7}{The first group of special cases of~(\ref {choinka})}{theorem.3.4}{}}
\newlabel{f2s-w3g}{{3.12}{7}{The first group of special cases of~(\ref {choinka})}{equation.3.12}{}}
\newlabel{ww3}{{3.13}{7}{The first group of special cases of~(\ref {choinka})}{equation.3.13}{}}
\newlabel{ww1}{{3.14}{7}{The first group of special cases of~(\ref {choinka})}{equation.3.14}{}}
\newlabel{ww2}{{3.15}{7}{The first group of special cases of~(\ref {choinka})}{equation.3.15}{}}
\citation{bradley}
\citation{sloan}
\newlabel{ww4}{{3.16}{8}{The first group of special cases of~(\ref {choinka})}{equation.3.16}{}}
\newlabel{ww5}{{3.17}{8}{The first group of special cases of~(\ref {choinka})}{equation.3.17}{}}
\newlabel{lem2.6}{{3.6}{8}{The first group of special cases of~(\ref {choinka})}{theorem.3.6}{}}
\newlabel{lem2.6-w1}{{3.19}{8}{The first group of special cases of~(\ref {choinka})}{equation.3.19}{}}
\newlabel{lem2.6-w2}{{3.20}{8}{The first group of special cases of~(\ref {choinka})}{equation.3.20}{}}
\newlabel{lem2.6-w3}{{3.21}{8}{The first group of special cases of~(\ref {choinka})}{equation.3.21}{}}
\newlabel{lem2.6-w4}{{3.22}{8}{The first group of special cases of~(\ref {choinka})}{equation.3.22}{}}
\newlabel{lem2.6-w5}{{3.23}{8}{The first group of special cases of~(\ref {choinka})}{equation.3.23}{}}
\newlabel{lem2.6-w6}{{3.24}{9}{The first group of special cases of~(\ref {choinka})}{equation.3.24}{}}
\newlabel{lem2.6-w7}{{3.25}{9}{The first group of special cases of~(\ref {choinka})}{equation.3.25}{}}
\newlabel{lem2.6-w8}{{3.26}{9}{The first group of special cases of~(\ref {choinka})}{equation.3.26}{}}
\newlabel{f2s-tw1}{{3.7}{9}{The first group of special cases of~(\ref {choinka})}{theorem.3.7}{}}
\newlabel{f2s-tw1-w-a}{{3.27}{9}{The first group of special cases of~(\ref {choinka})}{equation.3.27}{}}
\newlabel{f2s-tw1-w-b}{{3.28}{9}{The first group of special cases of~(\ref {choinka})}{equation.3.28}{}}
\newlabel{f2s-tw1-w-c}{{3.29}{9}{The first group of special cases of~(\ref {choinka})}{equation.3.29}{}}
\newlabel{f2s-tw1-w-d}{{3.30}{9}{The first group of special cases of~(\ref {choinka})}{equation.3.30}{}}
\newlabel{f2s-tw1-w-e}{{3.31}{9}{The first group of special cases of~(\ref {choinka})}{equation.3.31}{}}
\citation{wsw1}
\newlabel{f2s-tw1-w-f}{{3.32}{10}{The first group of special cases of~(\ref {choinka})}{equation.3.32}{}}
\newlabel{f2s-tw1-w-g}{{3.33}{10}{The first group of special cases of~(\ref {choinka})}{equation.3.33}{}}
\newlabel{f2s-tw1-w-h}{{3.34}{10}{The first group of special cases of~(\ref {choinka})}{equation.3.34}{}}
\citation{sloan}
\citation{sloan}
\citation{GrzymkowskiWitula}
\@writefile{toc}{\contentsline {section}{\numberline {4}The second group of special cases of\nobreakspace  {}(\ref  {choinka})}{11}{section.4}}
\newlabel{w4.1}{{4.1}{11}{The second group of special cases of~(\ref {choinka})}{equation.4.1}{}}
\newlabel{w4.2}{{4.2}{11}{The second group of special cases of~(\ref {choinka})}{equation.4.2}{}}
\newlabel{w4.3}{{4.3}{11}{The second group of special cases of~(\ref {choinka})}{equation.4.3}{}}
\newlabel{w4.4}{{4.4}{11}{The second group of special cases of~(\ref {choinka})}{equation.4.4}{}}
\newlabel{w4.5}{{4.5}{11}{The second group of special cases of~(\ref {choinka})}{equation.4.5}{}}
\newlabel{w4.6}{{4.6}{11}{The second group of special cases of~(\ref {choinka})}{equation.4.6}{}}
\newlabel{w3n.9}{{4.9}{11}{The second group of special cases of~(\ref {choinka})}{equation.4.9}{}}
\newlabel{f2s-tw2}{{4.2}{11}{The second group of special cases of~(\ref {choinka})}{theorem.4.2}{}}
\newlabel{f2s-tw2-w-a}{{4.10}{11}{The second group of special cases of~(\ref {choinka})}{equation.4.10}{}}
\newlabel{f2s-tw2-w-b}{{4.11}{12}{The second group of special cases of~(\ref {choinka})}{equation.4.11}{}}
\newlabel{f2s-tw2-w-c}{{4.12}{12}{The second group of special cases of~(\ref {choinka})}{equation.4.12}{}}
\newlabel{f2s-tw2-w-d}{{4.13}{12}{The second group of special cases of~(\ref {choinka})}{equation.4.13}{}}
\newlabel{f2s-tw2-w-e}{{4.14}{12}{The second group of special cases of~(\ref {choinka})}{equation.4.14}{}}
\newlabel{f2s-tw2-w-f}{{4.15}{12}{The second group of special cases of~(\ref {choinka})}{equation.4.15}{}}
\newlabel{w4.16a}{{4.16}{12}{The second group of special cases of~(\ref {choinka})}{equation.4.16}{}}
\newlabel{w4.17}{{4.17}{12}{The second group of special cases of~(\ref {choinka})}{equation.4.17}{}}
\newlabel{w4.18}{{4.18}{12}{The second group of special cases of~(\ref {choinka})}{equation.4.18}{}}
\newlabel{w4.19}{{4.19}{12}{The second group of special cases of~(\ref {choinka})}{equation.4.19}{}}
\newlabel{w4.20}{{4.20}{12}{The second group of special cases of~(\ref {choinka})}{equation.4.20}{}}
\newlabel{w4.21}{{4.21}{12}{The second group of special cases of~(\ref {choinka})}{equation.4.21}{}}
\newlabel{f2s-tw2a}{{4.3}{13}{The second group of special cases of~(\ref {choinka})}{theorem.4.3}{}}
\newlabel{w4.30}{{4.30}{13}{The second group of special cases of~(\ref {choinka})}{equation.4.30}{}}
\newlabel{w4.31}{{4.31}{13}{The second group of special cases of~(\ref {choinka})}{equation.4.31}{}}
\newlabel{w4.32}{{4.32}{13}{The second group of special cases of~(\ref {choinka})}{equation.4.32}{}}
\newlabel{w4.33}{{4.33}{13}{The second group of special cases of~(\ref {choinka})}{equation.4.33}{}}
\citation{Shevelev}
\citation{GrzymkowskiWitula}
\newlabel{w4.34}{{4.34}{14}{The second group of special cases of~(\ref {choinka})}{equation.4.34}{}}
\newlabel{w4.35}{{4.35}{14}{The second group of special cases of~(\ref {choinka})}{equation.4.35}{}}
\@writefile{toc}{\contentsline {section}{\numberline {5}Some Ramanujan-type formulas}{14}{section.5}}
\newlabel{w-srf1}{{5.1}{14}{Some Ramanujan-type formulas}{equation.5.1}{}}
\newlabel{w-srf2}{{5.2}{14}{Some Ramanujan-type formulas}{equation.5.2}{}}
\newlabel{w-fib1}{{5.3}{15}{Some Ramanujan-type formulas}{equation.5.3}{}}
\newlabel{w-fib2}{{5.4}{15}{Some Ramanujan-type formulas}{equation.5.4}{}}
\newlabel{w-fib3}{{5.5}{15}{Some Ramanujan-type formulas}{equation.5.5}{}}
\newlabel{w-fib4}{{5.6}{15}{Some Ramanujan-type formulas}{equation.5.6}{}}
\newlabel{w-fib5}{{5.7}{15}{Some Ramanujan-type formulas}{equation.5.7}{}}
\newlabel{w-fib6}{{5.8}{15}{Some Ramanujan-type formulas}{equation.5.8}{}}
\newlabel{w-fib7}{{5.9}{15}{Some Ramanujan-type formulas}{equation.5.9}{}}
\newlabel{w-fib8}{{5.10}{15}{Some Ramanujan-type formulas}{equation.5.10}{}}
\newlabel{w-fib9}{{5.11}{15}{Some Ramanujan-type formulas}{equation.5.11}{}}
\citation{Shevelev}
\citation{wsw1}
\@writefile{toc}{\contentsline {section}{\numberline {6}The sine-Fibonacci numbers of order $7$}{17}{section.6}}
\newlabel{f2s-r6-w1g}{{6.4}{17}{The sine-Fibonacci numbers of order $7$}{equation.6.4}{}}
\newlabel{w5.4.a}{{6.5}{17}{The sine-Fibonacci numbers of order $7$}{equation.6.5}{}}
\newlabel{w5.4.b}{{6.6}{17}{The sine-Fibonacci numbers of order $7$}{equation.6.6}{}}
\newlabel{w5.4.c}{{6.7}{17}{The sine-Fibonacci numbers of order $7$}{equation.6.7}{}}
\newlabel{w5.4.d}{{6.8}{17}{The sine-Fibonacci numbers of order $7$}{equation.6.8}{}}
\newlabel{f2s-r6-wdelta}{{6.9}{17}{The sine-Fibonacci numbers of order $7$}{equation.6.9}{}}
\newlabel{wz6.6}{{6.10}{18}{The sine-Fibonacci numbers of order $7$}{equation.6.10}{}}
\newlabel{wz6.8}{{6.12}{18}{The sine-Fibonacci numbers of order $7$}{equation.6.12}{}}
\newlabel{w5n.9}{{6.13}{18}{The sine-Fibonacci numbers of order $7$}{equation.6.13}{}}
\newlabel{w6.14}{{6.14}{18}{The sine-Fibonacci numbers of order $7$}{equation.6.14}{}}
\citation{wsw1}
\citation{wsw1}
\citation{wsw1}
\@writefile{toc}{\contentsline {section}{\numberline {7}Generating functions}{19}{section.7}}
\newlabel{roz-fun-two}{{7}{19}{Generating functions}{section.7}{}}
\newlabel{w7-15}{{7.15}{21}{Generating functions}{equation.7.15}{}}
\newlabel{w7-16}{{7.16}{21}{Generating functions}{equation.7.16}{}}
\@writefile{toc}{\contentsline {section}{\numberline {8}Jordan decomposition}{24}{section.8}}
\@writefile{toc}{\contentsline {section}{\numberline {9}Tables}{25}{section.9}}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces }}{25}{table.1}}
\newlabel{f2s-tab1}{{1}{25}{}{table.1}{}}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces }}{25}{table.2}}
\newlabel{f2s-tab7}{{2}{25}{}{table.2}{}}
\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces }}{26}{table.3}}
\newlabel{f2s-tab3}{{3}{26}{}{table.3}{}}
\@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces }}{26}{table.4}}
\newlabel{f2s-tab2}{{4}{26}{}{table.4}{}}
\@writefile{lot}{\contentsline {table}{\numberline {5}{\ignorespaces }}{27}{table.5}}
\newlabel{f2s-tab6}{{5}{27}{}{table.5}{}}
\@writefile{lot}{\contentsline {table}{\numberline {6}{\ignorespaces }}{27}{table.6}}
\newlabel{f2s-tab5}{{6}{27}{}{table.6}{}}
\bibcite{bradley}{1}
\@writefile{lot}{\contentsline {table}{\numberline {7}{\ignorespaces }}{28}{table.7}}
\newlabel{f2s-tab4}{{7}{28}{}{table.7}{}}
\@writefile{toc}{\contentsline {section}{\numberline {10}Acknowledgments}{28}{section.10}}
\bibcite{GrzymkowskiWitula}{2}
\bibcite{Ireland}{3}
\bibcite{Shevelev}{4}
\bibcite{ShklyarskyUSA}{5}
\bibcite{ShklyarskyMir}{6}
\bibcite{sloan}{7}
\bibcite{surowski}{8}
\bibcite{Watkins}{9}
\bibcite{wsw1}{10}
\bibcite{Yaglom}{11}
