A151002 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, 0, 0), (0, -1, 1), (1, 0, 1), (1, 1, -1), (1, 1, 1)}.

1, 2, 9, 38, 175, 817, 3888, 18706, 90741, 442632, 2169338, 10666288, 52587182, 259821034, 1285891645, 6373073347, 31622486634, 157058315801, 780692584245, 3883263652957, 19327173594696, 96240654982101, 479443040395988, 2389346456179473, 11911428087996838, 59398206424878578, 296273414137107748

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[-1 + i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150999 A151000 A151001 * A151003 A357547 A151004

Adjacent sequences: A150999 A151000 A151001 * A151003 A151004 A151005

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved