A149146 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, 1, 0), (1, -1, 0), (1, 1, 0)}.

1, 1, 4, 9, 38, 105, 465, 1445, 6576, 21967, 101705, 356515, 1671330, 6069369, 28713106, 107128585, 510306830, 1944968189, 9315345145, 36124224529, 173774490354, 683637900503, 3300446561596, 13142521887563, 63639686328278, 256061078049079, 1243072805687305, 5046866106336979, 24553914187626606

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, 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: A251689 A249101 A289157 * A149147 A149148 A149149

Adjacent sequences: A149143 A149144 A149145 * A149147 A149148 A149149

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved