A033440 Number of edges in 8-partite Turán graph of order n.

0, 0, 1, 3, 6, 10, 15, 21, 28, 35, 43, 52, 62, 73, 85, 98, 112, 126, 141, 157, 174, 192, 211, 231, 252, 273, 295, 318, 342, 367, 393, 420, 448, 476, 505, 535, 566, 598, 631, 665, 700, 735, 771, 808, 846, 885, 925

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,-1,0,0,0,0,0,1,-2,1).

Crossrefs

Cf. A002620, A000212, A033436, A033437, A033438, A033439, A033441, A033442, A033443, A033444. [Reinhard Zumkeller, Nov 30 2009]

Programs

Mathematica

CoefficientList[Series[- x^2 (x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)/((x - 1)^3 (x + 1) (x^2 + 1) (x^4 + 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 19 2013 *)
LinearRecurrence[{2,-1,0,0,0,0,0,1,-2,1},{0,0,1,3,6,10,15,21,28,35},50] (* Harvey P. Dale, Mar 23 2015 *)

Formula

a(n) = round( (7/16)*n(n-2) ) +0 or -1 depending on n: if there is k such 8k+4<=n<=8k+6 then a(n) = floor( (7/16)*n*(n-2)) otherwise a(n) = round( (7/16)*n(n-2)). E.g. because 8*2+4<=21<=8*2+6 a(n) = floor((7/16)*21*19) = floor(174, 5625)=174. - Benoit Cloitre, Jan 17 2002

a(n) = Sum_{k=0..n} A168181(k)*(n-k). [Reinhard Zumkeller, Nov 30 2009]

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

a(n) = Sum_{i=1..n} floor(7*i/8). - Wesley Ivan Hurt, Sep 12 2017