

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
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OFFSET

1,2


COMMENTS

Since separability is not invariant under graph isomorphism, all 2^(n(2n1))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), 1822.
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*n1))1.
a(n) = 2^(n*(n1))*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



