A033438 Number of edges in 6-partite Turán graph of order n.

0, 0, 1, 3, 6, 10, 15, 20, 26, 33, 41, 50, 60, 70, 81, 93, 106, 120, 135, 150, 166, 183, 201, 220, 240, 260, 281, 303, 326, 350, 375, 400, 426, 453, 481, 510, 540, 570, 601, 633, 666, 700, 735, 770, 806, 843, 881

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Apart from the initial term this is the elliptic troublemaker sequence R_n(1,6) (also sequence R_n(5,6)) in the notation of Stange (see Table 1, p.16). For other elliptic troublemaker sequences R_n(a,b) see the cross references below. - Peter Bala, Aug 12 2013

References

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

Links

• K. E. Stange, Integral points on elliptic curves and explicit valuations of division polynomials, arXiv:1108.3051 [math.NT], 2011-2014.
• 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,-1,0,0,0,1,-2,1).

Crossrefs

Differs from A025708(n)+1 at 31st position.

Cf. A002620, A000212, A033436, A033437, A033439, A033440, A033441, A033442, A033443, A033444. [From Reinhard Zumkeller, Nov 30 2009]

Elliptic troublemaker sequences: A007590 (= R_n(2,4)), A030511 (= R_n(2,6) = R_n(4,6)), A184535 (= R_n(2,5) = R_n(3,5)).

Programs

Mathematica

a[n_] := Floor[5n^2/12];
Table[a[n], {n, 0, 46}] (* Jean-François Alcover, Jul 31 2018, after Peter Bala *)

Formula

a(n) = Sum_{k=0..n} A097325(k)*(n-k). - Reinhard Zumkeller, Nov 30 2009

a(n) = +2*a(n-1) -a(n-2) +a(n-6) -2*a(n-7) +a(n-8).

G.f.: -x^2*(1+x+x^3+x^4+x^2) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^3 ).

a(n) = floor(5*n^2/12). - Peter Bala, Aug 12 2013

a(n) = Sum_{i=1..n} floor(5*i/6). - Wesley Ivan Hurt, Sep 12 2017