A151468 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, 0), (-1, 1), (0, 1), (1, -1), (1, 0)}.

1, 1, 3, 11, 38, 157, 658, 2892, 13148, 61075, 290365, 1402947, 6881643, 34184251, 171674635, 870572065, 4452380910, 22945034368, 119053691259, 621535445725, 3262935266824, 17216829337645, 91266703043512, 485870384685858, 2596760622362760, 13928930842625316, 74965797677694568, 404730005399499967

Offset

0,3

Links

Table of n, a(n) for n=0..27.

M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.

Mathematica

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] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A307571 A047096 A149060 * A289989 A295263 A018961

Adjacent sequences: A151465 A151466 A151467 * A151469 A151470 A151471

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved