A033437 Number of edges in 5-partite Turán graph of order n.

0, 0, 1, 3, 6, 10, 14, 19, 25, 32, 40, 48, 57, 67, 78, 90, 102, 115, 129, 144, 160, 176, 193, 211, 230, 250, 270, 291, 313, 336, 360, 384, 409, 435, 462, 490, 518, 547, 577, 608, 640, 672, 705, 739, 774, 810, 846, 883, 921, 960, 1000, 1040, 1081, 1123, 1166, 1210, 1254

Offset

0,4

Comments

Apart from the initial term this is the elliptic troublemaker sequence R_n(1,5) (also sequence R_n(4,5)) 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

R. L. Graham et al., eds., Handbook of Combinatorics, Vol. 2, p. 1234.

Links

Michael De Vlieger, Table of n, a(n) for n = 0..10000

Kevin Beanland, Hung Viet Chu, and Carrie E. Finch-Smith, Generalized Schreier sets, linear recurrence relation, Turán graphs, arXiv:2112.14905 [math.CO], 2021.

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

Wikipedia, Turán graph

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,1,-2,1).

Formula

G.f.: (x^5+x^4+x^3+x^2)/((1-x^5)*(1-x)^2).

a(n) = Sum_{k=0..n} A011558(k)*(n-k). - Reinhard Zumkeller, Nov 30 2009

a(n) = floor( 2n^2/5 ). - Wesley Ivan Hurt, Jun 20 2013

a(n) = Sum_{i=1..n} floor(4*i/5). - Wesley Ivan Hurt, Sep 12 2017

Mathematica

Table[Floor[2n^2/5], {n, 0, 60}]

Prog

(Magma) [2*n^2 div 5: n in [0..60]]; // Vincenzo Librandi, Apr 20 2015
(PARI) a(n)=2*n^2\5 \\ Charles R Greathouse IV, Apr 20 2015

Crossrefs

Cf. A002620, A000212, A033436, A033438, A033439, A033440, A033441, A033442, A033443, A033444. - 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)).

Cf. A279169.

Sequence in context: A253620 A282731 A134919 * A338335 A226185 A310071

Adjacent sequences: A033434 A033435 A033436 * A033438 A033439 A033440

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved