A033441 - OEIS

%I #44 Jul 07 2018 01:42:17

%S 0,0,1,3,6,10,15,21,28,36,44,53,63,74,86,99,113,128,144,160,177,195,

%T 214,234,255,277,300,324,348,373,399,426,454,483,513,544,576,608,641,

%U 675,710,746,783,821,860,900,940,981,1023,1066,1110,1155,1201,1248,1296

%N Number of edges in 9-partite Turán graph of order n.

%D Graham et al., Handbook of Combinatorics, Vol. 2, p. 1234.

%H Vincenzo Librandi, <a href="/A033441/b033441.txt">Table of n, a(n) for n = 0..1000</a>

%H Christian Meyer, <a href="/A033441/a033441.pdf">On conjecture no. 76 arising from the OEIS</a>, preprint, 2004. [cached copy]

%H Ralf Stephan, <a href="https://arxiv.org/abs/math/0409509">Prove or disprove: 100 conjectures from the OEIS</a>, arXiv:math/0409509 [math.CO], 2004.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TuranGraph.html">Turán Graph</a> [From _Reinhard Zumkeller_, Nov 30 2009]

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Tur%C3%A1n_graph">Turán graph</a> [From _Reinhard Zumkeller_, Nov 30 2009]

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1, 0, 0, 0, 0, 0, 0, 1, -2, 1).

%F G.f.: x*(1/(1-x) - 1/(1-x^9))/(1-x)^2. - _Ralf Stephan_, Mar 05 2004

%F a(n) = Sum_{k=0..n} A168182(k)*(n-k). - _Reinhard Zumkeller_, Nov 30 2009

%F 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

%F a(n) = Sum_{i=1..n} floor(8*i/9). - _Wesley Ivan Hurt_, Sep 12 2017

%t 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 *)

%t 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 *)

%Y Cf. A002620, A000212, A033436 - A033444. - _Reinhard Zumkeller_, Nov 30 2009

%K nonn,easy

%O 0,4

%A _N. J. A. Sloane_

%E More terms from _Vincenzo Librandi_, Oct 20 2013