A151240 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), (0, 0, 1), (1, 0, -1), (1, 0, 1), (1, 1, 1)}.

1, 3, 14, 64, 312, 1509, 7453, 36705, 182306, 904450, 4504678, 22425745, 111860659, 557873292, 2785109263, 13903649793, 69448593079, 346895872507, 1733313215705, 8660909647098, 43284667243118, 216329048923139, 1081301272953975, 5404905018332207, 27018500855114772, 135064878802668940

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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[-1 + i, j, 1 + k, -1 + n] + aux[i, 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: A060801 A292744 A151239 * A161131 A247978 A026592

Adjacent sequences: A151237 A151238 A151239 * A151241 A151242 A151243

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved