A150688 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, 1, -1), (0, 1, 1), (1, -1, -1), (1, 1, 1)}.

1, 2, 8, 26, 116, 454, 2100, 8894, 41900, 185078, 881964, 4001456, 19216082, 88779108, 428727854, 2006723990, 9731848516, 45999286078, 223817580500, 1065927621524, 5200294598270, 24915102118916, 121818280899766, 586473778140676, 2872722063604886, 13885401647814630, 68120539231017464

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, 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, -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: A150685 A150686 A150687 * A026660 A150689 A150690

Adjacent sequences: A150685 A150686 A150687 * A150689 A150690 A150691

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved