A033442 Number of edges in 10-partite Turán graph of order n.

0, 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 54, 64, 75, 87, 100, 114, 129, 145, 162, 180, 198, 217, 237, 258, 280, 303, 327, 352, 378, 405, 432, 460, 489, 519, 550, 582, 615, 649, 684, 720, 756, 793, 831, 870, 910, 951, 993, 1036, 1080, 1125, 1170, 1216, 1263

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

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,-1,0,0,0,0,0,0,0,1,-2,1).

Formula

a(n) = Sum_{k=0..n} A168184(k)*(n-k). [Reinhard Zumkeller, Nov 30 2009]

G.f.: -x^2*(x^2+x+1)*(x^6+x^3+1)/((x-1)^3*(x+1)*(x^4-x^3+x^2-x+1)*(x^4+x^3+x^2+x+1)). [Colin Barker, Aug 09 2012]

a(n) = Sum_{i=1..n} floor(9*i/10). - Wesley Ivan Hurt, Sep 12 2017

Mathematica

CoefficientList[Series[- x^2 (x^2 + x + 1) (x^6 + x^3 + 1)/((x - 1)^3 (x + 1) (x^4 - x^3 + x^2 - x + 1) (x^4 + x^3 + x^2 + x + 1)), {x, 0, 60}], x] (* Vincenzo Librandi, Oct 20 2013 *)

Crossrefs

Cf. A002620, A000212, A033436, A033437, A033438, A033439, A033440, A033441, A033443, A033444. [Reinhard Zumkeller, Nov 30 2009]

Sequence in context: A113168 A341192 A071817 * A105335 A130489 A211024

Adjacent sequences: A033439 A033440 A033441 * A033443 A033444 A033445

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Oct 20 2013

Status

approved