A148333 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, 0, 1), (1, -1, 0), (1, 0, -1)}.

1, 1, 2, 5, 14, 43, 145, 511, 1878, 7151, 27975, 111870, 456021, 1889917, 7940790, 33772677, 145191428, 630092620, 2757388326, 12157863845, 53970276037, 241044107881, 1082536970720, 4886346484996, 22158022408605, 100906064806922, 461316918159512, 2116643861301808, 9744189217604779

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[-1 + i, 1 + j, k, -1 + n] + aux[i, j, -1 + 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: A047970 A160701 A137551 * A271270 A201497 A122993

Adjacent sequences: A148330 A148331 A148332 * A148334 A148335 A148336

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved