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

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

Author

N. J. A. Sloane, Dec 04 2014

Keywords

• nonn
• more
• hard

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

• 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.

Crossrefs

Cf. A251418, A287064, A297572, A302486.

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

Extensions

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

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