A150282 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, 1), (1, 0, -1), (1, 0, 0)}.

1, 2, 6, 23, 90, 375, 1613, 7059, 31605, 142999, 654438, 3022635, 14049537, 65740592, 309093625, 1459725894, 6920762955, 32917564379, 157043754152, 751157909715, 3601267142252, 17302193782632, 83283828611094, 401582951212349, 1939410992759551, 9379689826072183, 45423799006293583, 220244969364798596

Offset

0,2

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + 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: A150281 A373311 A220899 * A150283 A150284 A150285

Adjacent sequences: A150279 A150280 A150281 * A150283 A150284 A150285

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved