A151458 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), (0, 1), (1, -1), (1, 0)}.

1, 1, 3, 8, 26, 88, 315, 1171, 4477, 17546, 70066, 284471, 1170797, 4876190, 20517751, 87111609, 372793818, 1606639972, 6968002247, 30392051069, 133241561658, 586871095960, 2595923416225, 11527409347635, 51371869596583, 229695131462288, 1030156580857929, 4633227156569544, 20893278979205582

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[i, 1 + 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: A161938 A189177 A151444 * A290351 A148815 A148816

Adjacent sequences: A151455 A151456 A151457 * A151459 A151460 A151461

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved