A251419 Domination number of the n-triangle grid graph TG_n.

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

Offset

1,3

Comments

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.

Links

Table of n, a(n) for n=1..38.

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

Formula

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

Crossrefs

Cf. A251418, A287064, A297572, A302486.

Sequence in context: A338375 A220838 A236294 * A036410 A008670 A338887

Adjacent sequences: A251416 A251417 A251418 * A251420 A251421 A251422

Keyword

nonn,more

Author

N. J. A. Sloane, Dec 04 2014

Extensions

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

Status

approved