A149777 - OEIS

A149777

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

1, 1, 5, 19, 79, 337, 1487, 6667, 30477, 140415, 654037, 3065781, 14464051, 68594987, 326693571, 1561823519, 7491695533, 36035788369, 173781740083, 839928505357, 4067694903275, 19735045783185, 95901855236635, 466718405307693, 2274377462525147, 11096773439811825, 54202198678000775, 265021403282703067

(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, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + 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: A160702 A149775 A149776 * A149778 A163609 A149779

Adjacent sequences: A149774 A149775 A149776 * A149778 A149779 A149780

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved