OFFSET
0,3
COMMENTS
Sequence given by the Hankel transform (see A001906 for definition) of A082147 = {1, 1, 9, 89, 945, 10577, 123129, 1476841, ...}; example: det([1, 1, 9, 89; 1, 9, 89, 945; 9, 89, 945, 10577; 89, 945, 10577, 123129]) = 8^6 = 262144.
The number of labeled multigraphs on n vertices such that (i) no self loops are allowed; (ii) all edges are painted in one of 3 colors; (iii) edges between any pair of vertices are painted in distinct colors. Note, this implies that there are at most 3 edges between any vertex pair. Also note there is no restriction on the color of edges incident to a common vertex. - Geoffrey Critzer, Jan 14 2020
FORMULA
a(n+1) is the determinant of n X n matrix M_(i, j) = binomial(8i, j).
Hankel transform of A059435. - Philippe Deléham, Sep 03 2006
MATHEMATICA
Table[2^(3*Binomial[n, 2]), {n, 0, 10}] (* Geoffrey Critzer, Nov 10 2011 *)
PROG
(PARI) a(n)=8^binomial(n, 2) \\ Charles R Greathouse IV, Jan 17 2012
(Magma) [2^(3*Binomial(n, 2)): n in [0..10]]; // G. C. Greubel, Feb 05 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Sep 01 2005
EXTENSIONS
a(10) corrected and a(11), a(12) from Georg Fischer, Apr 01 2022
STATUS
approved