A150930 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, 1), (0, 1, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 9, 33, 151, 647, 3018, 13621, 64646, 299168, 1435690, 6751801, 32625433, 155167697, 753314009, 3611917443, 17596490710, 84876974607, 414630697985, 2009149391658, 9836370273415, 47835367118857, 234612056537696, 1144260767327867, 5620493553263904, 27477926103350830, 135139447811815770

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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A150927 A150928 A150929 * A150931 A150932 A150933

Adjacent sequences: A150927 A150928 A150929 * A150931 A150932 A150933

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved