A148274 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, 1), (-1, 1, 1), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 4, 15, 40, 156, 477, 1997, 6657, 28924, 101735, 451962, 1652731, 7473701, 28162223, 128976650, 497426810, 2300644619, 9040435627, 42147544049, 168202296082, 789247856960, 3190840882314, 15052577627682, 61531648622295, 291587047647581, 1203360632633277, 5724533687324218

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A148271 A148272 A148273 * A148275 A148276 A148277

Adjacent sequences: A148271 A148272 A148273 * A148275 A148276 A148277

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved