A150725 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, 0), (-1, 1, -1), (0, 1, 0), (1, -1, 0), (1, 1, 1)}.

1, 2, 8, 28, 122, 496, 2256, 9758, 45330, 203168, 957032, 4384498, 20844492, 96970229, 464178852, 2183124710, 10503864829, 49816232559, 240665055849, 1148760209125, 5567836855452, 26714991278863, 129834147642432, 625571531369695, 3047129448094499, 14733209890996245, 71903582700108710

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, 1 + j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A150722 A150723 A150724 * A150726 A150727 A150728

Adjacent sequences: A150722 A150723 A150724 * A150726 A150727 A150728

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved