A150509 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), (0, -1, 1), (0, 1, 0), (0, 1, 1), (1, 1, -1)}.

1, 2, 7, 25, 102, 421, 1826, 8034, 36106, 164248, 755561, 3506429, 16389676, 77084134, 364407891, 1730410838, 8248698860, 39452993279, 189262877746, 910308265005, 4388634690019, 21202183937455, 102624744762164, 497583258709272, 2416313479214622, 11750478490536311, 57216349110310344, 278933752655062431

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, -1 + j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + 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: A150506 A150507 A150508 * A150510 A150511 A036784

Adjacent sequences: A150506 A150507 A150508 * A150510 A150511 A150512

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved