A148573 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, 0, -1), (0, 1, -1), (1, 0, 1)}.

1, 1, 3, 6, 20, 49, 172, 484, 1732, 5162, 18965, 59680, 220777, 715673, 2685204, 8953384, 33734326, 114539085, 435187894, 1503531596, 5729591256, 20035479823, 76771639039, 271669011838, 1043251861255, 3723452781558, 14354596419363, 51678596017672, 199560683860979, 723042091109072, 2800255744221056

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[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: A062164 A265112 A052408 * A148574 A005558 A138350

Adjacent sequences: A148570 A148571 A148572 * A148574 A148575 A148576

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved