A151054 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, 1), (0, 1, 0), (0, 1, 1), (1, 0, 0)}.

1, 3, 10, 37, 144, 587, 2447, 10373, 44719, 194771, 856606, 3796781, 16930030, 75941050, 342197870, 1548306802, 7031912521, 32035828812, 146378354245, 670564647033, 3078932397919, 14167738235588, 65317513081997, 301667548559747, 1395537609937826, 6465469216478910, 29996319173031686

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, j, k, -1 + n] + aux[i, -1 + 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, 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: A151052 A264231 A151053 * A052893 A052818 A299501

Adjacent sequences: A151051 A151052 A151053 * A151055 A151056 A151057

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved