A150556 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, 0), (0, 0, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 26, 105, 444, 1947, 8711, 39591, 182324, 848227, 3976086, 18761532, 89032134, 424423410, 2031081206, 9753336307, 46975045125, 226821209031, 1097703227863, 5323162897579, 25860225840988, 125831368964770, 613165370055901, 2991836251485650, 14615473211851948, 71475761295702573

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A150555 A151297 A052706 * A150557 A150558 A150559

Adjacent sequences: A150553 A150554 A150555 * A150557 A150558 A150559

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved