A150478 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), (1, -1, 0), (1, 0, 1), (1, 1, 0)}.

1, 2, 7, 25, 100, 388, 1632, 6786, 29287, 125113, 550128, 2406584, 10712694, 47474007, 213394404, 956947559, 4332774635, 19577754886, 89181193579, 405820090361, 1857550386541, 8495079111238, 39046539443296, 179406094099381, 827476958191883, 3815466697125080, 17651866802706634, 81662775275630439

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, -1 + k, -1 + n] + aux[-1 + 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: A333249 A151537 A074421 * A150479 A150480 A150481

Adjacent sequences: A150475 A150476 A150477 * A150479 A150480 A150481

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved