|
|
A109966
|
|
a(n) = 8^((n^2-n)/2).
|
|
3
|
|
|
1, 1, 8, 512, 262144, 1073741824, 35184372088832, 9223372036854775808, 19342813113834066795298816, 324518553658426726783156020576256, 43556142965880123323311949751266331066368, 46768052394588893382517914646921056628989841375232, 401734511064747568885490523085290650630550748445698208825344
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
LINKS
|
|
|
FORMULA
|
a(n+1) is the determinant of n X n matrix M_(i, j) = binomial(8i, j).
|
|
MATHEMATICA
|
|
|
PROG
|
(Magma) [2^(3*Binomial(n, 2)): n in [0..10]]; // G. C. Greubel, Feb 05 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|