A149754 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, 0), (1, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 83, 333, 1643, 7155, 35489, 161173, 801969, 3736501, 18625587, 88230789, 440281431, 2109661555, 10534432565, 50894814307, 254247117363, 1235902365797, 6175716789891, 30161603582603, 150743420895283, 738923672434885, 3693502675312573, 18158046286023841, 90770725819503389

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, -1 + j, 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: A023253 A149752 A149753 * A149755 A365878 A363163

Adjacent sequences: A149751 A149752 A149753 * A149755 A149756 A149757

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved