A033444 Number of edges in 12-partite Turán graph of order n.

0, 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 77, 89, 102, 116, 131, 147, 164, 182, 201, 221, 242, 264, 286, 309, 333, 358, 384, 411, 439, 468, 498, 529, 561, 594, 627, 661, 696, 732, 769, 807, 846, 886, 927, 969, 1012, 1056, 1100, 1145, 1191, 1238, 1286

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• Graham et al., Handbook of Combinatorics, Vol. 2, p. 1234.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Turán Graph [_Reinhard Zumkeller_, Nov 30 2009]
• Wikipedia, Turán graph [_Reinhard Zumkeller_, Nov 30 2009]
• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,0,0,0,1,-2,1).

Crossrefs

Cf. A002620, A000212, A033436, A033437, A033438, A033439, A033440, A033441, A033442, A033443. [Reinhard Zumkeller, Nov 30 2009]

Programs

Mathematica

CoefficientList[Series[- x^2 (x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)/((x - 1)^3 (x + 1) (x^2 - x + 1) (x^2 + 1) (x^2 + x + 1) (x^4 - x^2 + 1)), {x, 0, 60}], x] (* Vincenzo Librandi, Oct 20 2013 *)

Formula

a(n) = Sum_{k=0..n} A168185(k)*(n-k). [Reinhard Zumkeller, Nov 30 2009]

G.f.: -x^2*(x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)/((x-1)^3*(x+1)*(x^2-x+1)*(x^2+1)*(x^2+x+1)*(x^4-x^2+1)). [Colin Barker, Aug 09 2012]

a(n) = Sum_{i=1..n} floor(11*i/12). - Wesley Ivan Hurt, Sep 12 2017

Extensions

More terms from Vincenzo Librandi, Oct 20 2013