A149774 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), (0, 0, -1), (1, -1, 1), (1, 1, 1)}.

1, 1, 5, 19, 79, 329, 1427, 6303, 28543, 129815, 594231, 2743043, 12763939, 59677967, 280202503, 1320670335, 6246890303, 29642553197, 141049086189, 672738459979, 3215711195981, 15403293849855, 73919935038535, 355326202512773, 1710635425417343, 8247318167972133, 39815195511530137, 192451129350591837

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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[i, 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: A370194 A149773 A363548 * A160702 A149775 A149776

Adjacent sequences: A149771 A149772 A149773 * A149775 A149776 A149777

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved