A151503 - OEIS

A151503

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), (0, -1), (1, -1), (1, 0)}

%I #5 Dec 04 2016 13:57:04

%S 1,0,1,1,3,6,17,40,117,314,912,2667,7916,23963,73586,227611,715444,

%T 2262450,7223397,23261164,75343490,245847919,806839587,2661738663,

%U 8829581024,29418789715,98457806482,330890849398,1116135299721,3778754481148,12835824454442,43738283921029,149490351563243,512353843888497

%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), (0, -1), (1, -1), (1, 0)}

%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, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[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 0,5

%A _Manuel Kauers_, Nov 18 2008