A150449 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, 1, 1), (0, 0, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 24, 103, 422, 1897, 8252, 38343, 173194, 817272, 3772830, 18000984, 84356373, 405594146, 1921360373, 9287840494, 44344952313, 215279896503, 1034203427064, 5037048253756, 24314646830982, 118735070137360, 575379742866056, 2815825128273828, 13688879652455073, 67110918573106876

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, 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: A150447 A150448 A256492 * A150450 A150451 A150452

Adjacent sequences: A150446 A150447 A150448 * A150450 A150451 A150452

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved