A133791 Number of n X n binary matrices with every 1 adjacent to some 0 horizontally, vertically, diagonally or antidiagonally.

1, 15, 417, 50625, 24879489, 48231228511, 373654052856545, 11546079143118274625, 1422756868491071266637985, 699232611373976058162941025423, 1370556061582419558173913152072112161, 10714096395475651010921722651799661109404545

Offset

1,2

Comments

Number of dominating sets in the n X n king graph. - Andrew Howroyd, May 10 2017

Links

Stephan Mertens, Table of n, a(n) for n = 1..22 (first 18 terms from Christian Sievers)

Stephan Mertens, Domination Polynomials of the Grid, the Cylinder, the Torus, and the King Graph, arXiv:2408.08053 [math.CO], Aug 2024.

Eric Weisstein's World of Mathematics, Dominating Set

Eric Weisstein's World of Mathematics, King Graph

Wikipedia, Dominating set

Mathematica

A218663 = Import["https://oeis.org/A218663/b218663.txt", "Table"][[All, 2]];
a[n_] := A218663[[2 n^2 - 2 n + 1]];
Table[a[n], {n, 1, 11}] (* Jean-François Alcover, Sep 23 2019 *)

Crossrefs

Main diagonal of A218663.

Cf. A133515, A133556, A063443 (independent vertex sets).

Sequence in context: A216343 A184222 A069431 * A361284 A376872 A323781

Adjacent sequences: A133788 A133789 A133790 * A133792 A133793 A133794

Keyword

nonn

Author

R. H. Hardin, Jan 05 2008

Extensions

a(12) and beyond from Christian Sievers, Dec 03 2023

Status

approved