A150848 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, 1, 1), (1, 0, -1), (1, 1, 1)}.

1, 2, 8, 32, 140, 617, 2833, 13023, 61051, 286985, 1362993, 6490277, 31095769, 149316400, 719881023, 3477149010, 16841970459, 81704281033, 397171081932, 1933229347169, 9424536022275, 45996120235591, 224756168100779, 1099295755970498, 5382038943075592, 26371391810360854, 129323007857861106

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, -1 + 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: A150845 A150846 A150847 * A150849 A150850 A179469

Adjacent sequences: A150845 A150846 A150847 * A150849 A150850 A150851

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved