A150573 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), (0, -1, 1), (0, 1, 1), (1, 0, -1), (1, 0, 0)}.

1, 2, 7, 26, 108, 458, 2020, 9020, 41153, 189298, 882129, 4132643, 19524463, 92592779, 441695421, 2113051018, 10151937294, 48881656985, 236120064485, 1142560527886, 5542421758170, 26923764871934, 131045167290236, 638578415375738, 3116673093623562, 15226267885290104, 74482717847190263

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, j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + 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: A150570 A150571 A150572 * A150574 A150575 A150576

Adjacent sequences: A150570 A150571 A150572 * A150574 A150575 A150576

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved