The 2-Pascal Triangle and a Related Riordan Array
Yassine Otmani
Faculty of Mathematics
USTHB, RECITS Laboratory
P.O. Box 32
El Alia, 16111
Bab Ezzouar
Algiers
Algeria
Abstract:
In this paper, we determine the structure of the 2-Pascal triangle
and prove that it consists of even rows within a specific proper
Riordan array. We provide the generating functions for two identities
involving the coefficients of the triangle. As a consequence, we derive
some combinatorial identities, including the generating functions for
the sums of diagonal elements along a finite ray through the 2-Pascal
triangle. Finally, we determine the inverse transform of the trinomial
transform.
Full version: pdf,
dvi,
ps,
latex
(Concerned with sequences
A000032
A000073
A000129
A001333
A001644
A002605
A008277
A008287
A027907
A027914
A035343
A052948
A063260
A075115
A077828
A077835
A077843
A077846
A077943
A081179
A081336
A083878
A083882
A094531
A097893
A099463
A102001
A103770
A103771
A133872
A146559
A152107 and
A246437.)
Received September 17 2023; revised versions received November 9 2024; November 16 2024;
December 3 2024.
Published in Journal of Integer Sequences,
April 19 2025.
Return to
Journal of Integer Sequences home page