A151149 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), (0, 1, 1), (1, 0, 0), (1, 1, 1)}.

1, 3, 11, 47, 205, 927, 4255, 19801, 92979, 439999, 2094023, 10013335, 48069797, 231510505, 1118100716, 5412834139, 26258649825, 127617162326, 621219944598, 3028329600297, 14781495206522, 72233039396182, 353352855528410, 1730197214969105, 8479326622229208, 41588642299978089, 204130697543549986

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, j, k, -1 + n] + aux[i, -1 + j, -1 + 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: A151146 A151147 A151148 * A151150 A151151 A151152

Adjacent sequences: A151146 A151147 A151148 * A151150 A151151 A151152

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved