A150313 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, 1), (-1, 0, 1), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 21, 86, 308, 1334, 5105, 22767, 91337, 414498, 1709124, 7849083, 33074337, 153116559, 654915363, 3051009294, 13214018558, 61839195598, 270363305206, 1270075518621, 5598259111518, 26375004035402, 117014793372506, 552683257105742, 2466159918289860, 11671475968085655, 52329157562856000

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, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + 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: A150310 A150311 A150312 * A150314 A150315 A150316

Adjacent sequences: A150310 A150311 A150312 * A150314 A150315 A150316

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved