Journal of Integer Sequences, Vol. 24 (2021), Article 21.5.2

Sequences Involving Square Zig-Zag Shapes


László Németh
Institute of Mathematics
University of Sopron
Bajcsy Zs. u. 4
Sopron H9400
Hungary

László Szalay
Department of Mathematics
University J. Selye
Hradná str. 21
Komárno 945 01
Slovakia
and
Institute of Mathematics
University of Sopron
Bajcsy Zs. u. 4
Sopron H9400
Hungary

Abstract:

We define a so-called square k-zig-zag shape as a part of the regular square grid. Considering the shape as a k-zig-zag digraph, we give values of its vertices according to the number of the shortest paths from a base vertex. It provides several integer sequences, whose higher-order homogeneous recurrences are determined by the help of a special matrix recurrence.

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(Concerned with sequences A000001 A000012 A000045 A000079 A000244 A001519 A001906 A003462 A005021 A006053 A007070 A024175 A028495 A030191 A033190 A033191 A052975 A052993 A060557 A080937 A080938 A093131 A094256 A094667 A094788 A094789 A094790 A094803 A094806 A094811 A094825 A094826 A094827 A094828 A094829 A094865 A124302 A211216 A216263 A221863 A224422 A232801.)

Received December 16 2020; revised version received March 17 2021. Published in Journal of Integer Sequences, April 20 2021.

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