A151092 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, 0, 1), (0, 1, 0), (1, 0, 0), (1, 0, 1)}.

1, 3, 11, 43, 175, 756, 3305, 14745, 66861, 305534, 1412043, 6564204, 30697806, 144406873, 681755516, 3232121308, 15373877114, 73328686004, 350744115090, 1681368517796, 8077097896451, 38877607114420, 187439768335649, 905161861391191, 4377421380522272, 21197116816099867, 102772998419877823

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A151090 A059278 A151091 * A151093 A151094 A339043

Adjacent sequences: A151089 A151090 A151091 * A151093 A151094 A151095

Keyword

nonn,walk,changed

Author

Manuel Kauers, Nov 18 2008

Status

approved