A149068 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), (0, 1, 1), (1, -1, 1), (1, 0, -1)}.

1, 1, 3, 11, 42, 169, 721, 3105, 13838, 62047, 283633, 1303734, 6061730, 28318686, 133282890, 629750099, 2990908792, 14249878475, 68148765938, 326757727504, 1571225170941, 7571392176951, 36566846891408, 176917128336520, 857500703098429, 4162433708763959, 20234912112599861, 98493026288524495

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + 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: A117641 A200030 A084782 * A151088 A149069 A151089

Adjacent sequences: A149065 A149066 A149067 * A149069 A149070 A149071

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved