A301752 Clique covering number of the n-triangular grid graph.
1, 3, 4, 6, 8, 10, 13, 15, 19, 22, 26, 31, 35, 41, 46, 52, 58, 64, 71, 77, 85, 92, 100, 109, 117, 127, 136, 146, 156, 166, 177, 187, 199, 210, 222, 235, 247, 261, 274, 288, 302, 316, 331, 345, 361, 376, 392, 409, 425, 443, 460, 478, 496, 514, 533, 551, 571
Offset: 1
Keywords
Links
- Georg Fischer, Table of n, a(n) for n = 1..1000
- 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, Clique Covering Number.
- Eric Weisstein's World of Mathematics, Triangular Grid Graph.
- Eric Weisstein's World of Mathematics, Triangular Honeycomb King Graph.
- Index entries for linear recurrences with constant coefficients, signature (2,0,-1,-2,2,1,0,-2,1).
Crossrefs
Cf. A072065.
Programs
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Mathematica
Table[(Sqrt[3] (16 + 3 n (3 + n)) - 9 Cos[n Pi/6] + 2 Sqrt[3] Cos[2 n Pi/3] + 9 Cos[5 n Pi/6] + 9 Sin[n Pi/6] - 9 Sin[5 n Pi/6])/(18 Sqrt[3]), {n, 20}] (* Eric W. Weisstein, Apr 18 2019 *) LinearRecurrence[{2, 0, -1, -2, 2, 1, 0, -2, 1}, {1, 3, 4, 6, 8, 10, 13, 15, 19}, 20] (* Eric W. Weisstein, Apr 18 2019 *) CoefficientList[Series[(-1 - x + 2 x^2 + x^3 - x^4 - 2 x^5 + 2 x^7 - x^8)/((-1 + x)^3 (1 + x - x^3 + x^5 + x^6)), {x, 0, 20}], x] (* Eric W. Weisstein, Apr 18 2019 *)
Formula
a(n) ~ (n+1)*(n+2)/6. - Andrew Howroyd, Jun 27 2018
a(n) = 2*a(n-1) - a(n-3) - 2*a(n-4) + 2*a(n-5) + a(n-6) - 2*a(n-8) + a(n-9). - Eric W. Weisstein, Apr 18 2019
G.f.: x (-1 - x + 2*x^2 + x^3 - x^4 - 2*x^5 + 2*x^7 - x^8)/((-1 + x)^3*(1 + x - x^3 + x^5 + x^6)). - Eric W. Weisstein, Apr 18 2019
Extensions
a(11)-a(24) from Andrew Howroyd, Jun 27 2018
More terms from Georg Fischer, Jun 04 2019
Comments