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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

Table of n, a(n) for n=1..10.

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.)