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%I #8 Dec 27 2023 21:34:09
%S 1,0,2,2,11,27,101,348,1237,4752,17552,69635,269504,1085729,4351437,
%T 17775548,72934213,302080006,1259717600,5283979096,22304022387,
%U 94582158638,403155327233,1725391432093,7415018474585,31980782229030,138409663709656,600908838337016,2616559379817830
%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), (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 25, Tag 26.
%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[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 0,3
%A _Manuel Kauers_, Nov 18 2008