A291593 -id:A291593 - cp's OEIS frontend

A362576 Number of vertex cuts in the n X n rook complement graph.

0, 9, 114, 908, 5985, 35505, 196602, 1036992, 5277357, 26134385, 126677826, 603492444, 2834183937, 13150592889, 60391598610, 274863240992, 1241212143357, 5566202141193, 24807561785514, 109950785325900, 484883791129185, 2128652665933409, 9306262365861834

Offset: 1

Eric W. Weisstein, Apr 25 2023

nonn

Eric Weisstein's World of Mathematics, Rook Complement Graph
Eric Weisstein's World of Mathematics, Vertex Cut

Cf. A291593, A362575.

From Andrew Howroyd, Apr 30 2023: (Start)
a(n) = 2*n*(2^n-n-1) + n^2*(2^(n-1)-1)^2 + binomial(n,2)^2.
a(n) = 2^(n^2) - 1 - A291593(n). (End)

a(2) corrected and terms a(6) and beyond from Andrew Howroyd, Apr 30 2023

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

Original entry on oeis.org

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

Offset: 1

Eric W. Weisstein, Sep 14 2017

nonn

Eric Weisstein's World of Mathematics, Connected Dominating Set
Eric Weisstein's World of Mathematics, Rook Complement Graph

Cf. A291593, A292073.

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 *)

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

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

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

cp's OEIS Frontend

A362576 Number of vertex cuts in the n X n rook complement graph.

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