A150870 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, 0, 1), (0, -1, 1), (0, 1, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 8, 33, 145, 660, 3070, 14511, 69333, 334079, 1619791, 7892499, 38606071, 189434359, 931906421, 4594112238, 22687930940, 112209639076, 555661162474, 2754576110087, 13667816994863, 67871749544977, 337271248514160, 1676996069410049, 8342863297256909, 41524199235081691, 206760272344245310

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A255951 A150868 A150869 * A150871 A150872 A150873

Adjacent sequences: A150867 A150868 A150869 * A150871 A150872 A150873

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved