A150115 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, 0, 1), (0, 1, -1), (1, 0, 0), (1, 1, -1)}.

1, 2, 6, 19, 70, 272, 1102, 4603, 19689, 85905, 380419, 1706952, 7740063, 35416953, 163311951, 758082996, 3539424469, 16609301242, 78292331761, 370522059204, 1759756397921, 8384450205934, 40063002574731, 191928810878505, 921638909638874, 4435212118443270, 21385562185737670, 103301985771383536

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[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A150113 A150114 A199128 * A177477 A150116 A150117

Adjacent sequences: A150112 A150113 A150114 * A150116 A150117 A150118

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved