This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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. 2
 0, 32, 27648, 258473984, 34924795002880, 73692421593384353792, 2475385863878910456755126272, 1329190247836700110425361699261382656, 11417938846687390120116281062224453749176270848, 1569274711573306070659025854469940650153499575743856771072 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. 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 A245290(n) + A245291(n) = 2^(n*(2*n-1))-1. A245291(n) = 2^(n*(2*n-1))-2^(n*(n-1))*A229865(n). CROSSREFS Cf. A245290, A229865. Sequence in context: A230914 A232596 A123393 * A016937 A074800 A320859 Adjacent sequences:  A245288 A245289 A245290 * A245292 A245293 A245294 KEYWORD nonn AUTHOR Chai Wah Wu, Jul 16 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 20 03:51 EDT 2019. Contains 327210 sequences. (Running on oeis4.)