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 A033439 Number of edges in 7-partite Turán graph of order n. 13
 0, 0, 1, 3, 6, 10, 15, 21, 27, 34, 42, 51, 61, 72, 84, 96, 109, 123, 138, 154, 171, 189, 207, 226, 246, 267, 289, 312, 336, 360, 385, 411, 438, 466, 495, 525, 555, 586, 618, 651, 685, 720, 756, 792, 829, 867, 906, 946, 987, 1029, 1071, 1114, 1158, 1203, 1249 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Apart from the initial term this is the elliptic troublemaker sequence R_n(1,7) (also sequence R_n(6,7)) 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 Vincenzo Librandi, Table of n, a(n) for n = 0..1000 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,-1,0,0,0,0,1,-2,1). FORMULA a(n) = Sum_{k=0..n} A109720(k)*(n-k). [Reinhard Zumkeller, Nov 30 2009] G.f.: -x^2*(x+1)*(x^2-x+1)*(x^2+x+1)/((x-1)^3*(x^6+x^5+x^4+x^3+x^2+x+1)). [Colin Barker, Aug 09 2012] a(n) = floor(3*n^2/7). - Peter Bala, Aug 12 2013 a(0)=0, a(1)=0, a(2)=1, a(3)=3, a(4)=6, a(5)=10, a(6)=15, a(7)=21, a(8)=27, a(n)=2*a(n-1)-a(n-2)+a(n-7)-2*a(n-8)+a(n-9). - Harvey P. Dale, Mar 19 2015 a(n) = Sum_{i=1..n} floor(6*i/7). - Wesley Ivan Hurt, Sep 12 2017 MATHEMATICA CoefficientList[Series[- x^2 (x + 1) (x^2 - x + 1) (x^2 + x + 1)/((x - 1)^3 (x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)), {x, 0, 60}], x] (* Vincenzo Librandi, Oct 19 2013 *) LinearRecurrence[{2, -1, 0, 0, 0, 0, 1, -2, 1}, {0, 0, 1, 3, 6, 10, 15, 21, 27}, 60] (* Harvey P. Dale, Mar 19 2015 *) PROG (MAGMA) [Floor(3*n^2/7): n in [0..60]]; // Vincenzo Librandi, Oct 19 2013 CROSSREFS Cf. A002620, A000212, A033436, A033437, A033438, 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: A056150 A310081 A240443 * A194082 A061786 A171971 Adjacent sequences:  A033436 A033437 A033438 * A033440 A033441 A033442 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Vincenzo Librandi, Oct 19 2013 STATUS approved

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Last modified January 19 09:35 EST 2019. Contains 319306 sequences. (Running on oeis4.)