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A251419
Domination number of the n-triangle grid graph TG_n.
5
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
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
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, Dec 04 2014
EXTENSIONS
a(32)-a(38) from Andy Huchala, Mar 14 2024
STATUS
approved