A150961 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), (1, 0, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 9, 35, 165, 726, 3505, 16188, 79185, 374583, 1845761, 8859888, 43838438, 212462673, 1054088633, 5142459739, 25560670952, 125293685976, 623588353158, 3067597456458, 15281920264967, 75381010866285, 375793202132842, 1857628888719511, 9265761442827136, 45880612484672136, 228946542641546494

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[-1 + 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: A150958 A150959 A150960 * A150962 A150963 A150964

Adjacent sequences: A150958 A150959 A150960 * A150962 A150963 A150964

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved