A151486 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, 0), (-1, 1), (0, -1), (1, -1), (1, 0), (1, 1)}.

1, 0, 4, 5, 44, 113, 722, 2597, 14551, 62444, 332585, 1569633, 8236700, 41010951, 215319131, 1106939210, 5849532618, 30697255765, 163555279079, 870659496839, 4676999769135, 25163104334815, 136188957032710, 738854880092731, 4025575994504180, 21988824717744827, 120505304703519826, 662009237864120920

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

Crossrefs

Sequence in context: A041037 A041038 A239860 * A042383 A135799 A226648

Adjacent sequences: A151483 A151484 A151485 * A151487 A151488 A151489

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved