A150286 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), (0, 1, 0), (1, 0, 1)}.

1, 2, 6, 23, 92, 373, 1570, 6753, 29355, 129108, 573051, 2558595, 11492389, 51893937, 235229752, 1070025103, 4883515868, 22349033969, 102528034549, 471427909042, 2171989615757, 10025002682529, 46349526122276, 214622004998552, 995206476756639, 4620862990540902, 21481432464309450, 99975723576147778

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, j, -1 + k, -1 + n] + aux[i, -1 + 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, -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: A150283 A150284 A150285 * A150287 A150288 A150289

Adjacent sequences: A150283 A150284 A150285 * A150287 A150288 A150289

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved