A150429 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, 0, 0), (1, 1, 0)}.

1, 2, 7, 24, 97, 398, 1709, 7516, 33623, 152804, 702023, 3257118, 15220657, 71618594, 338740110, 1609684691, 7680446968, 36772243184, 176594075393, 850392064044, 4104756720361, 19855328329392, 96229304321799, 467172180895143, 2271541047696563, 11060726188373753, 53926404954551133, 263226318212262293

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, k, -1 + n] + aux[-1 + i, j, 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: A150426 A150427 A150428 * A150430 A363434 A150431

Adjacent sequences: A150426 A150427 A150428 * A150430 A150431 A150432

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved