A297572 -id:A297572 - cp's OEIS frontend

A287064 Number of dominating sets in the n-triangular grid graph.

1, 7, 45, 685, 20409, 1201941, 141147379, 32952001519, 15299378914117, 14127550190798059, 25944752255914338751, 94759724685920514675099, 688318811614248548827285461, 9943676783895971991257124086453, 285690558616920990681823749334591359, 16324365307318944099676240468111164604873

Offset: 0

Eric W. Weisstein, May 19 2017

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..20
Eric Weisstein's World of Mathematics, Dominating Set
Eric Weisstein's World of Mathematics, Triangular Grid Graph

Cf. A251419, A288721, A297572, A303049.

a(7)-a(11) from Andrew Howroyd, May 21 2017

Terms a(12) and beyond from Andrew Howroyd, Apr 18 2018

A251419 Domination number of the n-triangle grid graph TG_n having n vertices along each side.

Original entry on oeis.org

1, 1, 2, 3, 3, 5, 6, 7, 9, 10, 13, 15, 17, 19, 21, 24, 27, 30, 33, 36, 40, 43, 47, 51, 55, 59, 63, 68, 72, 77, 82, 87, 92, 97, 103, 108, 114, 120, 126

Offset: 1

N. J. A. Sloane, Dec 04 2014

a(n) is the minimum size of a dominating set of the triangular grid graph with n vertices along each side. - Andy Huchala, Mar 17 2024

Conjectured to equal floor((n^2 + 7n - 23)/14) for n >= 14. See A251418.

Andy Huchala, Python program.
Stan Wagon, Graph Theory Problems from Hexagonal and Traditional Chess, The College Mathematics Journal, Vol. 45, No. 4, September 2014, pp. 278-287.
Eric Weisstein's World of Mathematics, Domination Number.
Eric Weisstein's World of Mathematics, Triangular Grid Graph.
Eric Weisstein's World of Mathematics, Triangular Honeycomb King Graph.

Cf. A251418, A287064, A297572, A302486.

G.f.: (x^22 - x^21 - x^19 + 2*x^18 - x^17 - x^14 + 2*x^13 - 2*x^11 + 2*x^10 - 2*x^9 + x^8 + x^7 - 2*x^6 + x^5 - x^3 + x^2 - x)/(x^9 - 2*x^8 + x^7 - x^2 + 2*x - 1) (conjectured, equivalent to Wagon's conjectural formula from comments). - Andy Huchala, Mar 15 2024

a(32)-a(38) from Andy Huchala, Mar 14 2024

a(39) from Eric W. Weisstein, Dec 13 2024

A347639 Number of minimal dominating sets in the n-triangular grid graph.

Original entry on oeis.org

1, 3, 7, 27, 117, 1149, 9946, 147292, 2763601, 78714365, 2826640715

Offset: 0

Eric W. Weisstein, Sep 09 2021

Eric Weisstein's World of Mathematics, Minimal Dominating Set
Eric Weisstein's World of Mathematics, Triangular Grid Graph

Cf. A287064, A297572, A303228, A347724.

a(6)-a(10) from Andrew Howroyd, Jan 19 2022

cp's OEIS Frontend

A287064 Number of dominating sets in the n-triangular grid graph.

Views

Author

Keywords

Links

Crossrefs

Extensions

A251419 Domination number of the n-triangle grid graph TG_n having n vertices along each side.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

Extensions

A347639 Number of minimal dominating sets in the n-triangular grid graph.

Views

Author

Keywords

Links

Crossrefs

Extensions