A150294 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, 0), (-1, 0, 1), (0, 1, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 6, 23, 94, 403, 1762, 7864, 35690, 164108, 762357, 3569242, 16819681, 79692636, 379354005, 1812988443, 8694229731, 41817451066, 201659232415, 974725502503, 4721045311481, 22908166197986, 111341527565114, 541962528735588, 2641596154242981, 12891279928029972, 62981324355512110, 308015721936263522

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A150293 A370285 A371827 * A150295 A150296 A134064

Adjacent sequences: A150291 A150292 A150293 * A150295 A150296 A150297

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved