A150618 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), (0, 1, -1), (0, 1, 0), (1, 0, -1), (1, 1, 1)}.

1, 2, 7, 27, 113, 486, 2149, 9656, 44163, 203866, 950665, 4463267, 21077735, 100056766, 476950749, 2281932825, 10952902235, 52716305762, 254356037461, 1229925229735, 5958805157303, 28920214532890, 140580176883079, 684333358818358, 3335607948810023, 16277805042351034, 79522347806971445

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[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: A150615 A150616 A150617 * A150619 A150620 A150621

Adjacent sequences: A150615 A150616 A150617 * A150619 A150620 A150621

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved