A150949 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, 1, 0), (0, 0, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 9, 35, 153, 684, 3130, 14413, 67611, 318757, 1512407, 7216348, 34591322, 166310839, 802228575, 3880007130, 18806256468, 91330565750, 444334925781, 2165001991383, 10563165653576, 51602579070086, 252366487312174, 1235448917020900, 6053663874898523, 29687789962059097, 145703830206882092

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -1 + j, -1 + k, -1 + 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, 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: A110224 A363549 A150948 * A150950 A150951 A150952

Adjacent sequences: A150946 A150947 A150948 * A150950 A150951 A150952

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved