A149410 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, 0, 0), (-1, 0, 1), (1, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 12, 52, 197, 887, 3686, 17039, 74498, 350257, 1580535, 7514894, 34622615, 165947569, 775826792, 3740678741, 17676527734, 85615386144, 407871219683, 1982550001834, 9504673256898, 46331928211929, 223240994258588, 1090772943473217, 5277092832609988, 25834617528759960, 125405601347310656

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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A149408 A125529 A149409 * A149411 A149412 A259274

Adjacent sequences: A149407 A149408 A149409 * A149411 A149412 A149413

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved