The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A290949 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A290949

Number of connected dominating sets in the n X n rook complement graph.
(history; published version)

#27 by Bruno Berselli at Mon Jan 15 10:29:15 EST 2018

STATUS

proposed

approved

#26 by Eric W. Weisstein at Mon Jan 15 08:03:52 EST 2018

STATUS

editing

proposed

#25 by Eric W. Weisstein at Mon Jan 15 08:03:46 EST 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 *)

STATUS

approved

editing

#24 by Joerg Arndt at Mon Jan 15 03:09:43 EST 2018

STATUS

proposed

approved

#23 by Andrew Howroyd at Sun Jan 14 23:45:10 EST 2018

STATUS

editing

proposed

#22 by Andrew Howroyd at Sun Jan 14 23:43:07 EST 2018

DATA

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

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

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.

KEYWORD

nonn,more

nonn

EXTENSIONS

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

STATUS

approved

editing

#21 by Susanna Cuyler at Thu Sep 14 18:16:27 EDT 2017

STATUS

proposed

approved

#20 by Eric W. Weisstein at Thu Sep 14 11:05:46 EDT 2017

STATUS

editing

proposed

#19 by Eric W. Weisstein at Thu Sep 14 11:05:44 EDT 2017

NAME

allocated for Eric W. Weisstein

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

DATA

1, 0, 325, 63899, 33542996

OFFSET

1,3

LINKS

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

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

KEYWORD

allocated

nonn,more

AUTHOR

Eric W. Weisstein, Sep 14 2017

STATUS

approved

editing

#18 by Eric W. Weisstein at Thu Sep 14 11:05:44 EDT 2017

NAME

allocated for Eric W. Weisstein

KEYWORD

recycled

allocated