A148408 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, 0), (0, 0, -1), (0, 1, 0), (1, -1, 1)}.

1, 1, 2, 5, 17, 55, 182, 643, 2384, 8953, 34333, 133626, 530606, 2133524, 8644984, 35438834, 146590627, 610689574, 2563048975, 10817091462, 45933788835, 196112722486, 840788136757, 3621782958317, 15663569148973, 67984934057062, 296161171799370, 1294062201532022, 5671755196756937

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[i, -1 + j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A263678 A133510 A191640 * A002692 A148409 A149980

Adjacent sequences: A148405 A148406 A148407 * A148409 A148410 A148411

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved