A149973 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, 1, 0), (1, 0, -1), (1, 0, 0)}.

1, 2, 5, 16, 56, 204, 780, 3099, 12594, 52123, 219696, 939511, 4061334, 17733255, 78151761, 347048149, 1551225434, 6976462330, 31550130733, 143365879422, 654323444492, 2998603009552, 13792688901614, 63654344411450, 294688265919191, 1368229743361834, 6369561861745394, 29725712375089444

Offset

0,2

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, 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: A176332 A191241 A052708 * A149974 A149975 A149976

Adjacent sequences: A149970 A149971 A149972 * A149974 A149975 A149976

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved