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%I #59 Sep 08 2022 08:44:51
%S 0,0,1,3,6,10,14,19,25,32,40,48,57,67,78,90,102,115,129,144,160,176,
%T 193,211,230,250,270,291,313,336,360,384,409,435,462,490,518,547,577,
%U 608,640,672,705,739,774,810,846,883,921,960,1000,1040,1081,1123,1166,1210,1254
%N Number of edges in 5-partite Turán graph of order n.
%C 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
%D R. L. Graham et al., eds., Handbook of Combinatorics, Vol. 2, p. 1234.
%H Michael De Vlieger, <a href="/A033437/b033437.txt">Table of n, a(n) for n = 0..10000</a>
%H Kevin Beanland, Hung Viet Chu, and Carrie E. Finch-Smith, <a href="https://arxiv.org/abs/2112.14905">Generalized Schreier sets, linear recurrence relation, Turán graphs</a>, arXiv:2112.14905 [math.CO], 2021.
%H K. E. Stange, <a href="https://arxiv.org/abs/1108.3051">Integral points on elliptic curves and explicit valuations of division polynomials</a> arXiv:1108.3051 [math.NT], 2011-2014.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TuranGraph.html">Turán Graph</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Tur%C3%A1n_graph">Turán graph</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,1,-2,1).
%F G.f.: (x^5+x^4+x^3+x^2)/((1-x^5)*(1-x)^2).
%F a(n) = Sum_{k=0..n} A011558(k)*(n-k). - _Reinhard Zumkeller_, Nov 30 2009
%F a(n) = floor( 2n^2/5 ). - _Wesley Ivan Hurt_, Jun 20 2013
%F a(n) = Sum_{i=1..n} floor(4*i/5). - _Wesley Ivan Hurt_, Sep 12 2017
%t Table[Floor[2n^2/5],{n,0,60}]
%o (Magma) [2*n^2 div 5: n in [0..60]]; // _Vincenzo Librandi_, Apr 20 2015
%o (PARI) a(n)=2*n^2\5 \\ _Charles R Greathouse IV_, Apr 20 2015
%Y Cf. A002620, A000212, A033436, A033438, A033439, A033440, A033441, A033442, A033443, A033444. - _Reinhard Zumkeller_, Nov 30 2009
%Y 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)).
%Y Cf. A279169.
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_
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