%I
%S 1,1,3,10,35,138,566,2431,10780,49067,228355,1081997,5207905,25403962,
%T 125377203,625176432,3145870880,15959346050,81557403529,419547453308,
%U 2171222736256,11298086327362,59085844684247,310430932981503,1637929078223208,8676341846872322,46128302460092674,246081020287578117
%N Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(1, 1), (1, 1), (0, 1), (0, 1), (1, 1), (1, 0)}
%H M. BousquetMÃ©lou 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, j, 1 + 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, 1 + j, 1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]
%K nonn,walk
%O 0,3
%A _Manuel Kauers_, Nov 18 2008
