A290949 Number of connected dominating sets in the n X n rook complement graph.

1, 0, 325, 63899, 33542996, 68719407048, 562949953031061, 18446744073707483871, 2417851639229258338870480, 1267650600228229401496650962840, 2658455991569831745807614120307387245, 22300745198530623141535718272648360299106443

Offset

1,3

Links

Table of n, a(n) for n=1..12.

Eric Weisstein's World of Mathematics, Connected Dominating Set

Eric Weisstein's World of Mathematics, Rook Complement Graph

Formula

a(n) = 2^(n^2) - 2*n*(2^n - 1) + n^2 - 2*n^2*(2^(n-1)-1)^2 + n^2*(n-1)^2 - 3*binomial(n,2)^2 - 1 for n > 1. - Andrew Howroyd, Jan 14 2018

Mathematica

Table[If[n == 1, 1, 2^(n^2) - 2 n (2^n - 1) + n^2 (1 - 2 (2^(n - 1) - 1)^2 + (n - 1)^2) - 3 Binomial[n, 2]^2 - 1], {n, 20}] (* Eric W. Weisstein, Jan 15 2018 *)

Prog

(PARI) a(n) = if(n==1, 1, 2^(n^2) - 2*n*(2^n - 1) + n^2 - 2*n^2*(2^(n-1)-1)^2 + n^2*(n-1)^2 - 3*binomial(n, 2)^2 - 1); \\ Andrew Howroyd, Jan 14 2018

Crossrefs

Cf. A291593, A292073.

Sequence in context: A340462 A166220 A121000 * A048909 A097739 A203188

Adjacent sequences: A290946 A290947 A290948 * A290950 A290951 A290952

Keyword

nonn

Author

Eric W. Weisstein, Sep 14 2017

Extensions

a(6)-a(12) from Andrew Howroyd, Jan 14 2018

Status

approved