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

0,4

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

Table of n, a(n) for n=0..46.

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).

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

Mathematica

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

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)).

Sequence in context: A168101 A310080 A027920 * A037452 A047800 A109443

Adjacent sequences: A033435 A033436 A033437 * A033439 A033440 A033441

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved