A150007 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, -1), (0, 1, 1), (1, 0, 0)}.

1, 2, 5, 17, 60, 221, 842, 3296, 13055, 52736, 215995, 892130, 3721084, 15641114, 66149907, 281448936, 1204203656, 5175356782, 22336615979, 96782596868, 420774787816, 1835193720702, 8028162116450, 35214500581325, 154849465504524, 682526378223530, 3014873000908227, 13344302448375870

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, k, -1 + n] + aux[i, -1 + j, -1 + 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, 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: A150004 A150005 A150006 * A150008 A150009 A150010

Adjacent sequences: A150004 A150005 A150006 * A150008 A150009 A150010

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved