A150519 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, 0, 1), (1, -1, 1), (1, 0, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 25, 103, 430, 1895, 8429, 38455, 176689, 823170, 3855727, 18212344, 86380177, 411945954, 1970859842, 9464998343, 45570229510, 220010368400, 1064345370439, 5159793445294, 25055027916931, 121862457504495, 593515381648381, 2894453376030765, 14131579800582367, 69069300067238427

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[-1 + i, j, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150516 A150517 A150518 * A150520 A150521 A150522

Adjacent sequences: A150516 A150517 A150518 * A150520 A150521 A150522

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved