A150924 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, 0), (0, -1, 1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 33, 147, 639, 2866, 13157, 60394, 282158, 1322334, 6237030, 29606868, 140835340, 673495024, 3227042178, 15511352835, 74730396260, 360726910545, 1744897446220, 8452908393449, 41016055196881, 199283762807080, 969486346848564, 4721843121299076, 23021442861098952, 112352317288238442

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, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A150921 A150922 A150923 * A150925 A150926 A150927

Adjacent sequences: A150921 A150922 A150923 * A150925 A150926 A150927

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved