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A109966 a(n) = 8^((n^2-n)/2). 3

%I #42 Sep 08 2022 08:45:19

%S 1,1,8,512,262144,1073741824,35184372088832,9223372036854775808,

%T 19342813113834066795298816,324518553658426726783156020576256,

%U 43556142965880123323311949751266331066368,46768052394588893382517914646921056628989841375232,401734511064747568885490523085290650630550748445698208825344

%N a(n) = 8^((n^2-n)/2).

%C 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.

%C 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

%F a(n+1) is the determinant of n X n matrix M_(i, j) = binomial(8i, j).

%F Hankel transform of A059435. - _Philippe Deléham_, Sep 03 2006

%t Table[2^(3*Binomial[n,2]),{n,0,10}] (* _Geoffrey Critzer_, Nov 10 2011 *)

%o (PARI) a(n)=8^binomial(n,2) \\ _Charles R Greathouse IV_, Jan 17 2012

%o (Magma) [2^(3*Binomial(n,2)): n in [0..10]]; // _G. C. Greubel_, Feb 05 2018

%Y Cf. A006125, A047656, A053763, A053764, A059435, A082147, A109345, A109354, A109493.

%K nonn,easy

%O 0,3

%A _Philippe Deléham_, Sep 01 2005

%E a(10) corrected and a(11), a(12) from _Georg Fischer_, Apr 01 2022

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)