A148284 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 0, 0), (-1, 1, 0), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 5, 12, 32, 97, 282, 870, 2870, 9215, 30571, 106328, 361324, 1256426, 4523643, 15971258, 57343994, 211680313, 767950799, 2823061650, 10618284888, 39319704544, 147172286980, 561739600196, 2113692222212, 8025292111327, 30995394823367, 118139661528722, 453789274312738, 1769748668161067

Offset

0,3

Links

Table of n, a(n) for n=0..30.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A076822 A143657 A014326 * A148285 A115523 A176336

Adjacent sequences: A148281 A148282 A148283 * A148285 A148286 A148287

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved