A149803 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, 0), (-1, 0, 1), (1, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 19, 89, 377, 1831, 8307, 40565, 189303, 933393, 4444391, 21975921, 105828359, 525171549, 2551014001, 12677085287, 61924637965, 308237631627, 1512454238183, 7534170662857, 37085838737413, 184899111189783, 912527989327283, 4551642348259077, 22507604314668835, 112321975016457063

Offset

0,3

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, -1 + j, 1 + k, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A184513 A149801 A149802 * A259204 A149804 A340994

Adjacent sequences: A149800 A149801 A149802 * A149804 A149805 A149806

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved