A151480 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, 1), (0, -1), (1, -1), (1, 0), (1, 1)}.

1, 0, 3, 3, 30, 65, 434, 1384, 7847, 30749, 162310, 714126, 3667411, 17254387, 88023109, 431259271, 2206144905, 11092437052, 57117060880, 292296895499, 1516673564569, 7861699769116, 41103663171314, 215169677630869, 1132925333732196, 5977775212622087, 31674824100293083, 168233379153239317

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

Crossrefs

Sequence in context: A100651 A124244 A351990 * A096351 A367890 A344934

Adjacent sequences: A151477 A151478 A151479 * A151481 A151482 A151483

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved