A148916 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, 0, 1), (-1, 1, 1), (1, -1, 0), (1, 0, 0), (1, 1, -1)}.

1, 1, 3, 8, 33, 116, 516, 2063, 9554, 40942, 194045, 867281, 4170657, 19162172, 93044027, 435704224, 2129890888, 10110771458, 49665401778, 238154054194, 1174043836070, 5672872958902, 28041860704509, 136297267469379, 675146477214983, 3296794913796290, 16357334853181910, 80170121258985704

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A258690 A091831 A284963 * A148917 A120892 A195499

Adjacent sequences: A148913 A148914 A148915 * A148917 A148918 A148919

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved