cp's OEIS Frontend

A029656 Numbers in the (2,1)-Pascal triangle A029653 that are different from 1.

%I A029656 #24 Jul 02 2025 16:01:56
%S A029656 2,2,3,2,5,4,2,7,9,5,2,9,16,14,6,2,11,25,30,20,7,2,13,36,55,50,27,8,2,
%T A029656 15,49,91,105,77,35,9,2,17,64,140,196,182,112,44,10,2,19,81,204,336,
%U A029656 378,294,156,54,11,2,21,100,285,540,714,672,450,210,65,12,2,23,121,385
%N A029656 Numbers in the (2,1)-Pascal triangle A029653 that are different from 1.
%D A029656 D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; triangle on page 6, numerators.
%H A029656 Michael De Vlieger, <a href="/A029656/b029656.txt">Table of n, a(n) for n = 1..11325</a> (rows 1 <= n <= 150)
%H A029656 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlternatingSignMatrix.html">Alternating Sign Matrix.</a>
%H A029656 D. Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/DaveRobbins/guess.html">Dave Robbins's Art of Guessing</a>, Adv. in Appl. Math. 34 (2005), 939-954.
%F A029656 From _Thomas Baruchel_, Jun 26 2018: (Start)
%F A029656 a(n,k) = (binomial(n+2,k+1) + binomial(n+1,k) + binomial(n,k) - binomial(n,k+1))/2.
%F A029656 a(n,k) = binomial(n-1,k-1) + binomial(n-1,k) + binomial(n,k-1) + binomial(n,k). (End)
%e A029656 Triangle begins:
%e A029656   2;
%e A029656   2,  3;
%e A029656   2,  5,  4;
%e A029656   2,  7,  9,  5;
%e A029656   2,  9, 16, 14,  6;
%e A029656   2, 11, 25, 30, 20,  7;
%e A029656   ...
%t A029656 Table[(Binomial[n + 2, k + 1] + Binomial[n + 1, k] + Binomial[n, k] - Binomial[n, k + 1])/2, {n, 0, 11}, {k, 0, n}] // Flatten (* _Michael De Vlieger_, Jun 29 2018 *)
%Y A029656 Cf. A048601, A029638.
%K A029656 nonn,tabl
%O A029656 1,1
%A A029656 _Mohammad K. Azarian_
%E A029656 More terms from _James Sellers_