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

0,4

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).

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

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 *)

Crossrefs

Cf. A002620, A000212, A033436 - A033444. - Reinhard Zumkeller, Nov 30 2009

Sequence in context: A231684 A363777 A108923 * A338334 A107082 A267238

Adjacent sequences: A033438 A033439 A033440 * A033442 A033443 A033444

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Oct 20 2013

Status

approved