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Number of edges in 11-partite Turán graph of order n.
10

%I #28 Sep 13 2017 03:12:56

%S 0,0,1,3,6,10,15,21,28,36,45,55,65,76,88,101,115,130,146,163,181,200,

%T 220,240,261,283,306,330,355,381,408,436,465,495,525,556,588,621,655,

%U 690,726,763,801,840,880,920,961,1003,1046,1090,1135,1181,1228,1276

%N Number of edges in 11-partite Turán graph of order n.

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

%H Vincenzo Librandi, <a href="/A033443/b033443.txt">Table of n, a(n) for n = 0..1000</a>

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

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

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,0,0,0,0,1,-2,1).

%F a(n) = Sum_{k=0..n} A145568(k)*(n-k). [_Reinhard Zumkeller_, Nov 30 2009]

%F G.f.: -x^2*(x+1)*(x^4-x^3+x^2-x+1)*(x^4+x^3+x^2+x+1)/((x-1)^3*(x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)). [_Colin Barker_, Aug 09 2012]

%F a(n) = Sum_{i=1..n} floor(10*i/11). - _Wesley Ivan Hurt_, Sep 12 2017

%t CoefficientList[Series[- x^2 (x + 1) (x^4 - x^3 + x^2 - x + 1) (x^4 + x^3 + x^2 + x + 1)/((x - 1)^3 (x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)), {x, 0, 60}], x] (* _Vincenzo Librandi_, Oct 20 2013 *)

%Y Cf. A002620, A000212, A033436, A033437, A033438, A033439, A033440, A033441, A033442, 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