OFFSET
1,2
COMMENTS
From Andrew Howroyd, Aug 30 2017: (Start)
The vertex sets inducing disconnected subgraphs are:
- two or more vertices taken from a single row or column,
- any vertex combined with at least one from the same row and at least one from the same column,
- four vertices forming the corners of a rectangle. (End)
LINKS
Eric Weisstein's World of Mathematics, Connected Graph
Eric Weisstein's World of Mathematics, Rook Complement Graph
Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph
FORMULA
a(n) = 2^(n^2) - 2*n*(2^n-n-1) - n^2*(2^(n-1)-1)^2 - binomial(n,2)^2 - 1. - Andrew Howroyd, Aug 30 2017
MATHEMATICA
Table[2^(n^2) - 2 n (2^n - n - 1) - n^2 (2^(n - 1) - 1)^2 - Binomial[n, 2]^2 - 1, {n, 10}]
PROG
(PARI) a(n) = 2^(n^2) - 2*n*(2^n-n-1) - n^2*(2^(n-1)-1)^2 - binomial(n, 2)^2 - 1; \\ Andrew Howroyd, Aug 30 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Aug 27 2017
EXTENSIONS
a(6)-a(12) from Andrew Howroyd, Aug 30 2017
STATUS
approved