A149876 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, 1), (0, 1, -1), (1, 0, 0), (1, 1, 0)}.

1, 2, 5, 14, 42, 136, 451, 1546, 5407, 19191, 69191, 251867, 925820, 3430082, 12789590, 47974023, 180826904, 684611939, 2601928569, 9922514404, 37956726661, 145587887723, 559808213755, 2157340447787, 8330424172574, 32227003874198, 124881479757620, 484665714314689, 1883659790434405

Offset

0,2

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, 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A129086 A035052 A148330 * A165146 A360708 A148331

Adjacent sequences: A149873 A149874 A149875 * A149877 A149878 A149879

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved