A150291 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, 0), (0, 1, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 6, 23, 93, 395, 1715, 7628, 34515, 158261, 733349, 3425978, 16116745, 76247726, 362489048, 1730424090, 8290157145, 39839993841, 191980105704, 927330790608, 4488871016747, 21770316366607, 105762645905230, 514596727823666, 2507295439786995, 12231867958048600, 59742116644828109, 292096657897667247

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, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, j, 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: A326355 A012866 A150290 * A150292 A191721 A150293

Adjacent sequences: A150288 A150289 A150290 * A150292 A150293 A150294

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved