A151262 - OEIS

A151262

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

%I #4 Dec 04 2016 13:56:59

%S 1,1,3,6,18,47,141,416,1278,3983,12616,40475,131461,430548,1423924,

%T 4741118,15896509,53622384,181826538,619678461,2121171010,7290531452,

%U 25152947775,87076167883,302422286268,1053449686642,3679700846025,12886585101117,45238465102771,159171202374935,561236984775150,1982888741975501

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

%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>.

%H A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, <a href="http://arxiv.org/abs/0811.2899">ArXiv 0811.2899</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]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]

%K nonn,walk

%O 0,3

%A _Manuel Kauers_, Nov 18 2008