A290949 - OEIS

%I #27 Jan 15 2018 10:29:15

%S 1,0,325,63899,33542996,68719407048,562949953031061,

%T 18446744073707483871,2417851639229258338870480,

%U 1267650600228229401496650962840,2658455991569831745807614120307387245,22300745198530623141535718272648360299106443

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConnectedDominatingSet.html">Connected Dominating Set</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RookComplementGraph.html">Rook Complement Graph</a>

%F 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

%t 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 *)

%o (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

%Y Cf. A291593, A292073.

%K nonn

%O 1,3

%A _Eric W. Weisstein_, Sep 14 2017

%E a(6)-a(12) from _Andrew Howroyd_, Jan 14 2018