A148229 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, 0), (-1, 1, -1), (-1, 1, 0), (1, -1, 1), (1, 0, 0)}.

1, 1, 2, 4, 13, 33, 118, 347, 1341, 4318, 17545, 59856, 251495, 896183, 3859528, 14217556, 62388697, 235860592, 1050383993, 4055229753, 18275493427, 71790138056, 326702931541, 1302162074045, 5974359609738, 24109258946617, 111379884904233, 454295827860432, 2111201191123406, 8691686866081354

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A320424 A148227 A148228 * A148230 A227808 A148231

Adjacent sequences: A148226 A148227 A148228 * A148230 A148231 A148232

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved