A151462 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), (1, 1)}.

1, 1, 3, 8, 27, 89, 320, 1158, 4347, 16510, 63903, 249952, 989110, 3947056, 15878333, 64296723, 261931840, 1072616649, 4413123474, 18233286270, 75619434417, 314696837489, 1313747904446, 5500152407820, 23087645330262, 97148591427302, 409700045646219, 1731398744266320, 7331054076146476

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, -1 + j, -1 + 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}]

Crossrefs

Sequence in context: A148833 A210680 A121650 * A145967 A145792 A148834

Adjacent sequences: A151459 A151460 A151461 * A151463 A151464 A151465

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved