A150557 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, 1, 1), (0, 1, -1), (0, 1, 1), (1, 0, 1)}.

1, 2, 7, 26, 106, 433, 1840, 7940, 34600, 152415, 677408, 3026920, 13601908, 61423330, 278412139, 1266274777, 5777664180, 26431866609, 121211063067, 557094467005, 2565518805088, 11835880142484, 54695962523709, 253149015388344, 1173298821523358, 5445202284648577, 25301849449310989, 117702463118949106

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, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A151297 A052706 A150556 * A150558 A150559 A150560

Adjacent sequences: A150554 A150555 A150556 * A150558 A150559 A150560

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved