A149040 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, 10, 36, 130, 520, 2067, 8494, 35300, 149423, 635968, 2745231, 11899039, 52046711, 228659377, 1010809064, 4485019664, 19996926503, 89433261856, 401494048103, 1807338533648, 8160308932476, 36932017463770, 167565419553694, 761831452631384, 3470970716552609, 15842684133176819

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, 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: A246975 A047122 A047107 * A055989 A329533 A102871

Adjacent sequences: A149037 A149038 A149039 * A149041 A149042 A149043

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved