A148439 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, 0)}.

1, 1, 2, 6, 15, 43, 143, 447, 1457, 5153, 17712, 62226, 228307, 826403, 3045356, 11463886, 42915761, 163162575, 626421084, 2403106726, 9332107293, 36397643689, 142264226087, 560927157537, 2216454163673, 8789867068979, 35060453041676, 140072687401512, 561842105897395, 2261924959908545

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[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: A303833 A373455 A148438 * A151515 A264746 A052870

Adjacent sequences: A148436 A148437 A148438 * A148440 A148441 A148442

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved