A251418 Floor((n^2+7n-23)/14).

-2, -2, -1, 0, 1, 2, 3, 5, 6, 8, 10, 12, 14, 16, 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, 132, 138, 145, 151, 158, 165, 172, 179, 186, 194, 201, 209, 217, 225, 233, 241, 250, 258, 267, 276

Offset: 0

Author

N. J. A. Sloane, Dec 04 2014

Keywords

• sign
• easy

Comments

This is conjectured to be the value of the dominance number of the triangle grid graph for n >= 14 - see A251419.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Stan Wagon, Graph Theory Problems from Hexagonal and Traditional Chess, The College Mathematics Journal, Vol. 45, No. 4, September 2014 pp. 278-287.
• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,1,-2,1).

Crossrefs

Cf. A251419.

Programs

Magma

[Floor((n^2+7*n-23)/14): n in [0..60]]; // Vincenzo Librandi, Dec 04 2014

Mathematica

Table[Floor[(n^2 + 7 n - 23) / 14], {n, 0, 80}] (* Vincenzo Librandi, Dec 04 2014 *)
LinearRecurrence[{2,-1,0,0,0,0,1,-2,1},{-2,-2,-1,0,1,2,3,5,6},60] (* Harvey P. Dale, Mar 19 2020 *)

PARI

Vec((3*x^8-3*x^7-x^2-2*x+2)/((x-1)^3*(x^6+x^5+x^4+x^3+x^2+x+1)) + O(x^100)) \\ Colin Barker, Jul 10 2015

Formula

G.f.: (3*x^8-3*x^7-x^2-2*x+2) / ((x-1)^3*(x^6+x^5+x^4+x^3+x^2+x+1)). - Colin Barker, Jul 10 2015

Extensions

More terms from Vincenzo Librandi, Dec 04 2014