A149396 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, 0), (-1, 1, 1), (0, 0, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 12, 50, 187, 801, 3367, 14750, 64496, 288283, 1298078, 5916459, 27107847, 125107445, 580279403, 2704828242, 12656086712, 59445058605, 280159509962, 1324504668796, 6278619362700, 29835818846267, 142094119428556, 678102617877031, 3242027299595844, 15526944664613450, 74482919169897600

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, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A104708 A149394 A149395 * A149397 A034488 A149398

Adjacent sequences: A149393 A149394 A149395 * A149397 A149398 A149399

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved