A149452 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, 0), (0, 1, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 13, 49, 190, 797, 3360, 14534, 63886, 284896, 1282848, 5829638, 26690801, 122989106, 569876645, 2653240162, 12405690763, 58222972007, 274173721826, 1294976257690, 6133081638010, 29118225874467, 138556467358426, 660664529658206, 3156133476745489, 15103784291215723, 72396182383167108

Offset

0,3

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A097948 A096971 A149451 * A140660 A149453 A149454

Adjacent sequences: A149449 A149450 A149451 * A149453 A149454 A149455

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved