A150971 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), (-1, 1, 0), (0, 1, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 9, 36, 158, 717, 3309, 15375, 72555, 344182, 1640966, 7863210, 37826596, 182448229, 882425744, 4277829024, 20776458752, 101076141067, 492491511517, 2402811356306, 11736894220444, 57393337393508, 280928335727393, 1376301299048225, 6748197431155125, 33112331353842749, 162589309192203086

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, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A073156 A150969 A150970 * A150972 A150973 A150974

Adjacent sequences: A150968 A150969 A150970 * A150972 A150973 A150974

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved