A150289 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, 1), (1, 0, 0), (1, 1, -1)}.

1, 2, 6, 23, 92, 386, 1665, 7347, 32998, 150231, 691195, 3206754, 14984744, 70444527, 332881927, 1579979745, 7527828960, 35986754865, 172545311966, 829485969096, 3997025967601, 19301064888858, 93379586216132, 452555731106801, 2196718896415187, 10678245472578013, 51975160155428364, 253288779232041951

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[-1 + i, j, k, -1 + n] + aux[i, -1 + j, -1 + 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: A150286 A150287 A150288 * A326355 A012866 A150290

Adjacent sequences: A150286 A150287 A150288 * A150290 A150291 A150292

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved