A150795 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, 0), (0, 0, 1), (1, 0, -1), (1, 1, 1)}

1, 2, 8, 31, 130, 562, 2504, 11349, 52133, 242147, 1134569, 5349564, 25364039, 120833817, 577944794, 2773523513, 13349920977, 64426566906, 311621092011, 1510283142011, 7332950131233, 35661675760230, 173681079039219, 846987755340579, 4135471231344979, 20213711486229043, 98900945363007922

Offset

0,2

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, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A027073 A150793 A150794 * A027078 A150796 A150797

Adjacent sequences: A150792 A150793 A150794 * A150796 A150797 A150798

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved