%I #8 Dec 27 2023 01:20:57
%S 1,0,0,1,2,0,5,26,28,42,369,908,1122,5773,23119,42716,117508,549438,
%T 1479612,3367843,13480787,46542736,115686395,371629486,1402498101,
%U 4078027887,11785376915,42758254550,140673861443,410211643221,1373805039590,4780700411490,14793100980164,47088191339857,163599002479471
%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 10, Tag 14.
%H 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>.
%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 0,5
%A _Manuel Kauers_, Nov 18 2008