A150972 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, 1), (1, 1, 1)}.

1, 2, 9, 36, 159, 719, 3324, 15454, 72896, 345861, 1649363, 7902249, 38014529, 183362565, 886800001, 4298873305, 20878467212, 101568952226, 494874891454, 2414381195687, 11793084852520, 57666389951926, 282257772798245, 1382781421358439, 6779805885912587, 33266687008728500, 163343872291235027

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, -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: A150969 A150970 A150971 * A150973 A150974 A248438

Adjacent sequences: A150969 A150970 A150971 * A150973 A150974 A150975

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved