A150473 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, 0, 1), (0, 1, 1), (1, 0, -1)}.

1, 2, 7, 25, 99, 404, 1710, 7397, 32598, 145601, 657960, 3000643, 13791325, 63806466, 296873158, 1388007345, 6517379983, 30717477390, 145259967469, 688974178087, 3276592282215, 15620378854390, 74630234665050, 357278349533557, 1713537162879366, 8232110673000747, 39609752128758538, 190860289784929949

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, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 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: A150470 A150471 A150472 * A150474 A150475 A150476

Adjacent sequences: A150470 A150471 A150472 * A150474 A150475 A150476

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved