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 A245290 Number of normalized graph Laplacian matrices of nonempty labeled graphs of 2n vertices that are separable in C^2 X C^n as density matrices in quantum mechanics. 1
 1, 31, 5119, 9961471, 259577085951, 94554701453852671, 494214691850093043122175, 37747948215762478445361018961919, 42694960288928350006693371507341885702143, 722273364120299921501331975953872089285372151857151 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Since separability is not invariant under graph isomorphism, all 2^(n(2n-1))-1 nonzero Laplacian matrices are treated as different.  A nonzero Laplacian matrix different from the complete graph is separable in C^2 X C^n if and only if its complement is.  Since the complete graph is separable, this means that a(n) is odd for all n. LINKS C. W. Wu, Conditions for separability in generalized Laplacian matrices and diagonally dominant matrices as density matrices, Physics Letters A, 351 (2006), 18-22. C. W. Wu, Graphs whose normalized Laplacian matrices are separable as density matrices in quantum mechanics, arXiv:1407.5663, 2014. FORMULA a(n) + A245291(n) = 2^(n*(2*n-1))-1. a(n) = 2^(n*(n-1))*A229865(n)-1. CROSSREFS Cf. A245291, A229865. Sequence in context: A115736 A110848 A214109 * A090681 A297767 A065756 Adjacent sequences:  A245287 A245288 A245289 * A245291 A245292 A245293 KEYWORD nonn AUTHOR Chai Wah Wu, Jul 16 2014 STATUS approved

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Last modified August 25 05:06 EDT 2019. Contains 326318 sequences. (Running on oeis4.)