A033441 Number of edges in 9-partite Turán graph of order n.
0, 0, 1, 3, 6, 10, 15, 21, 28, 36, 44, 53, 63, 74, 86, 99, 113, 128, 144, 160, 177, 195, 214, 234, 255, 277, 300, 324, 348, 373, 399, 426, 454, 483, 513, 544, 576, 608, 641, 675, 710, 746, 783, 821, 860, 900, 940, 981, 1023, 1066, 1110, 1155, 1201, 1248, 1296
Offset: 0
References
- Graham et al., Handbook of Combinatorics, Vol. 2, p. 1234.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Christian Meyer, On conjecture no. 76 arising from the OEIS, preprint, 2004. [cached copy]
- Ralf Stephan, Prove or disprove: 100 conjectures from the OEIS, arXiv:math/0409509 [math.CO], 2004.
- Eric Weisstein's World of Mathematics, Turán Graph [From _Reinhard Zumkeller_, Nov 30 2009]
- Wikipedia, Turán graph [From _Reinhard Zumkeller_, Nov 30 2009]
- Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,1,-2,1).
Crossrefs
Programs
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Mathematica
CoefficientList[Series[- x^2 (x + 1) (x^2 + 1) (x^4 + 1)/((x - 1)^3 (x^2 + x + 1) (x^6 + x^3 + 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 20 2013 *) LinearRecurrence[{2, -1, 0, 0, 0, 0, 0, 0, 1, -2, 1},{0, 0, 1, 3, 6, 10, 15, 21, 28, 36, 44},55] (* Ray Chandler, Aug 04 2015 *)
Formula
G.f.: x*(1/(1-x) - 1/(1-x^9))/(1-x)^2. - Ralf Stephan, Mar 05 2004
a(n) = Sum_{k=0..n} A168182(k)*(n-k). - Reinhard Zumkeller, Nov 30 2009
G.f.: -x^2*(x+1)*(x^2+1)*(x^4+1)/((x-1)^3*(x^2+x+1)*(x^6+x^3+1)). - Colin Barker, Aug 09 2012
a(n) = Sum_{i=1..n} floor(8*i/9). - Wesley Ivan Hurt, Sep 12 2017
Extensions
More terms from Vincenzo Librandi, Oct 20 2013