A150697 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, 0, -1), (-1, 0, 1), (1, 0, 0), (1, 1, 1)}.

1, 2, 8, 26, 120, 445, 2106, 8302, 40075, 163934, 797561, 3341834, 16370003, 69800886, 343163275, 1482329691, 7311311272, 31907997150, 157698550081, 693887774764, 3435657381930, 15220483718537, 75456187238874, 336186700906527, 1668558215343475, 7470397836029163, 37108210390926633, 166837300163396705

Offset

0,2

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A150694 A150695 A150696 * A150698 A150699 A150700

Adjacent sequences: A150694 A150695 A150696 * A150698 A150699 A150700

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved