A149490 - OEIS

A149490

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

1, 1, 4, 14, 55, 229, 982, 4323, 19432, 88523, 408097, 1899317, 8904553, 42017023, 199307875, 949663789, 4542475867, 21800444196, 104929173198, 506335199834, 2448829379333, 11867219402240, 57612620658000, 280146125980324, 1364211290739354, 6651960449096001, 32474079720857800, 158707717042022479

(list; graph; refs; listen; history; text; internal format)

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A280208 A088655 A302288 * A304977 A143406 A329777

Adjacent sequences: A149487 A149488 A149489 * A149491 A149492 A149493

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved