A150619 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, 0, 0), (0, 1, 0), (1, 0, -1), (1, 1, 1)}.

1, 2, 7, 27, 113, 488, 2153, 9694, 44271, 204554, 953315, 4475849, 21137241, 100325552, 478223145, 2287958851, 10981230887, 52852954902, 255010311345, 1233090218839, 5974213577387, 28995287070748, 140948424165699, 686143437201718, 3344529967847247, 16321924207377448, 79740804980498977

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, -1 + j, k, -1 + n] + aux[1 + i, 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: A150616 A150617 A150618 * A150620 A150621 A150622

Adjacent sequences: A150616 A150617 A150618 * A150620 A150621 A150622

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved