cp's OEIS Frontend

A151347 Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of n steps taken from {(-1, 0), (-1, 1), (0, -1), (0, 1), (1, -1)}.

%I A151347 #15 Oct 22 2019 04:19:28
%S A151347 1,0,1,1,3,8,19,65,177,611,1928,6648,22928,80851,292343,1063611,
%T A151347 3957406,14818681,56339994,215943994,836246604,3265240671,12848804154,
%U A151347 50936668789,203235590343,816070826188,3295317218038,13379003847708,54588942258042,223782828113783,921414594957514,3809576782931810
%N A151347 Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of n steps taken from {(-1, 0), (-1, 1), (0, -1), (0, 1), (1, -1)}.
%H A151347 Michael De Vlieger, <a href="/A151347/b151347.txt">Table of n, a(n) for n = 0..500</a>
%H A151347 A. Bostan, K. Raschel, B. Salvy, <a href="http://dx.doi.org/10.1016/j.jcta.2013.09.005">Non-D-finite excursions in the quarter plane</a>, J. Comb. Theory A 121 (2014) 45-63, Table 1 Tag 35, Tag 39.
%H A151347 M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, <a href="http://arxiv.org/abs/0810.4387">ArXiv 0810.4387</a>.
%H A151347 Colin Defant, <a href="https://arxiv.org/abs/1904.10451">Motzkin Intervals and Valid Hook Configurations</a>, arXiv:1904.10451 [math.CO], 2019.
%H A151347 Maya Sankar, <a href="https://arxiv.org/abs/1910.08895">Further Bijections to Pattern-Avoiding Valid Hook Configurations</a>, arXiv:1910.08895 [math.CO], 2019.
%t A151347 aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[aux[0, 0, n], {n, 0, 25}]
%K A151347 nonn,walk
%O A151347 0,5
%A A151347 _Manuel Kauers_, Nov 18 2008