A148386 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, 0, -1), (1, 0, -1), (1, 0, 0)}.

1, 1, 2, 5, 16, 51, 169, 564, 2046, 7548, 28355, 106596, 411047, 1612830, 6399150, 25472182, 102322757, 415580010, 1702115777, 6999101160, 28909694958, 120178955216, 502695571138, 2110933288776, 8891383171714, 37597524503463, 159682804500152, 680544335825135, 2907712571031676

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, j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, 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: A148385 A205501 A118973 * A148387 A121651 A054660

Adjacent sequences: A148383 A148384 A148385 * A148387 A148388 A148389

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved