A148610 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, 1), (-1, 0, 0), (-1, 1, -1), (1, -1, 0), (1, 0, 1)}.

1, 1, 3, 6, 21, 53, 202, 573, 2276, 6970, 28580, 91972, 384766, 1287580, 5472167, 18839174, 81030265, 285642073, 1240356821, 4454674973, 19496366549, 71145867213, 313392200589, 1158861586203, 5133032314943, 19201412716941, 85448486537833, 322825409515699, 1442522497615599, 5497959947697567

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A148607 A148608 A148609 * A148611 A148612 A098511

Adjacent sequences: A148607 A148608 A148609 * A148611 A148612 A148613

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved