|
%I #45 Mar 18 2024 12:53:12
%S 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,
%T 63,68,72,77,82,87,92,97,103,108,114,120
%N Domination number of the n-triangle grid graph TG_n.
%C 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
%C Conjectured to equal floor((n^2 + 7n - 23)/14) for n >= 14. See A251418.
%H Andy Huchala, <a href="/A251419/a251419.py.txt">Python program</a>.
%H Stan Wagon, <a href="http://www.jstor.org/stable/10.4169/college.math.j.45.4.278">Graph Theory Problems from Hexagonal and Traditional Chess</a>, The College Mathematics Journal, Vol. 45, No. 4, September 2014, pp. 278-287
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DominationNumber.html">Domination Number</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TriangularGridGraph.html">Triangular Grid Graph</a>
%F 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
%Y Cf. A251418, A287064, A297572, A302486.
%K nonn,more
%O 1,3
%A _N. J. A. Sloane_, Dec 04 2014
%E a(32)-a(38) from _Andy Huchala_, Mar 14 2024
|
