A148879 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, 0, 1), (0, 1, 1), (1, -1, -1), (1, 0, -1)}.

1, 1, 3, 8, 30, 95, 385, 1401, 5815, 22659, 96885, 392671, 1710249, 7147647, 31498799, 134580859, 598984123, 2600652988, 11666192756, 51299141640, 231548223922, 1028545822270, 4666617519716, 20898981088272, 95237695053924, 429391511451396, 1964082138100110, 8905342679048126, 40866113426475180

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, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + 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: A344899 A148877 A148878 * A148880 A148881 A148882

Adjacent sequences: A148876 A148877 A148878 * A148880 A148881 A148882

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved