cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A245291 Number of normalized graph Laplacian matrices of nonempty labeled graphs of 2n vertices that are entangled in C^2 x C^n as density matrices in quantum mechanics.

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%I A245291 #19 Jul 24 2023 04:53:31
%S A245291 0,32,27648,258473984,34924795002880,73692421593384353792,
%T A245291 2475385863878910456755126272,1329190247836700110425361699261382656,
%U A245291 11417938846687390120116281062224453749176270848,1569274711573306070659025854469940650153499575743856771072
%N A245291 Number of normalized graph Laplacian matrices of nonempty labeled graphs of 2n vertices that are entangled in C^2 x C^n as density matrices in quantum mechanics.
%C A245291 Since entanglement is not invariant under graph isomorphism, all 2^(n(2n-1))-1 nonzero Laplacian matrices are treated as different.  A nonzero Laplacian matrix not equal to the complete graph is entangled in C^2 x C^n if and only if its complement is.  Since the complete graph is not entangled, this means that a(n) is even for all n.
%H A245291 Chai Wah Wu, <a href="http://dx.doi.org/10.1016/j.physleta.2005.10.049">Conditions for separability in generalized Laplacian matrices and diagonally dominant matrices as density matrices</a>, Physics Letters A, 351 (2006), 18-22.
%H A245291 Chai Wah Wu, <a href="http://arxiv.org/abs/1407.5663">Graphs whose normalized Laplacian matrices are separable as density matrices in quantum mechanics</a>, arXiv:1407.5663 [quant-ph], 2014.
%F A245291 A245290(n) + a(n) = 2^(n*(2*n-1))-1.
%F A245291 a(n) = 2^(n*(2*n-1))-2^(n*(n-1))*A229865(n).
%Y A245291 Cf. A245290, A229865.
%K A245291 nonn
%O A245291 1,2
%A A245291 _Chai Wah Wu_, Jul 16 2014