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%I #15 Dec 27 2023 21:35:58
%S 1,0,1,2,2,14,21,76,252,566,2282,6248,19958,69356,205129,720868,
%T 2340178,7692570,26681224,87814024,302838250,1035805496,3526054994,
%U 12286338876,42255768876,147090631152,513835481206,1790785075144,6298459417432,22120204885156,77965202090697,275780508039312,975587671958542
%N 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, -1), (-1, 0), (0, -1), (1, 1)}.
%H 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 5, Tag 16.
%H M. Bousquet-Mélou and M. Mishna, <a href="https://arxiv.org/abs/0810.4387">Walks with small steps in the quarter plane</a>, arXiv:0810.4387 [math.CO], 2008-2009.
%H Igor Pak, <a href="https://arxiv.org/abs/1803.06636">Complexity problems in enumerative combinatorics</a>, arXiv:1803.06636 [math.CO], 2018.
%t 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[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[aux[0, 0, n], {n, 0, 25}]
%K nonn,walk
%O 0,4
%A _Manuel Kauers_, Nov 18 2008
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