A150388 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, -1, 1), (-1, 1, 1), (1, 0, 1), (1, 1, 0)}.

1, 2, 7, 23, 102, 375, 1745, 6878, 32644, 133432, 640941, 2686025, 13008572, 55465855, 270114683, 1167116596, 5706990946, 24912842259, 122187282951, 537859897295, 2644295665648, 11719823403199, 57728318531618, 257340579052914, 1269573706580594, 5687351829395149, 28094740408209420, 126394025609794392

Offset

0,2

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, 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, -1 + 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: A150386 A150387 A265797 * A073344 A038119 A006986

Adjacent sequences: A150385 A150386 A150387 * A150389 A150390 A150391

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved