A148888 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, 1), (-1, 1, 1), (0, -1, 1), (1, 0, -1), (1, 0, 0)}.

1, 1, 3, 8, 30, 104, 413, 1627, 6738, 28291, 121351, 527845, 2325348, 10350338, 46493978, 210439523, 959042601, 4396353397, 20259252722, 93795603600, 436053315743, 2034850056215, 9527769028756, 44749410126415, 210766594872031, 995244645976326, 4710672278535226, 22344931695751350

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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[-1 + i, 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, 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: A148886 A148887 A221537 * A151440 A213860 A360991

Adjacent sequences: A148885 A148886 A148887 * A148889 A148890 A148891

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved