A033440 Number of edges in 8-partite Turán graph of order n.

0, 0, 1, 3, 6, 10, 15, 21, 28, 35, 43, 52, 62, 73, 85, 98, 112, 126, 141, 157, 174, 192, 211, 231, 252, 273, 295, 318, 342, 367, 393, 420, 448, 476, 505, 535, 566, 598, 631, 665, 700, 735, 771, 808, 846, 885, 925

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

Formula

a(n) = round( (7/16)*n(n-2) ) +0 or -1 depending on n: if there is k such 8k+4<=n<=8k+6 then a(n) = floor( (7/16)*n*(n-2)) otherwise a(n) = round( (7/16)*n(n-2)). E.g. because 8*2+4<=21<=8*2+6 a(n) = floor((7/16)*21*19) = floor(174, 5625)=174. - Benoit Cloitre, Jan 17 2002

a(n) = Sum_{k=0..n} A168181(k)*(n-k). [Reinhard Zumkeller, Nov 30 2009]

G.f.: -x^2*(x^6+x^5+x^4+x^3+x^2+x+1)/((x-1)^3*(x+1)*(x^2+1)*(x^4+1)). [Colin Barker, Aug 09 2012]

a(n) = Sum_{i=1..n} floor(7*i/8). - Wesley Ivan Hurt, Sep 12 2017

Mathematica

CoefficientList[Series[- x^2 (x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)/((x - 1)^3 (x + 1) (x^2 + 1) (x^4 + 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 19 2013 *)
LinearRecurrence[{2, -1, 0, 0, 0, 0, 0, 1, -2, 1}, {0, 0, 1, 3, 6, 10, 15, 21, 28, 35}, 50] (* Harvey P. Dale, Mar 23 2015 *)

Crossrefs

Cf. A002620, A000212, A033436, A033437, A033438, A033439, A033441, A033442, A033443, A033444. [Reinhard Zumkeller, Nov 30 2009]

Sequence in context: A161208 A109444 A124157 * A067525 A130487 A231684

Adjacent sequences: A033437 A033438 A033439 * A033441 A033442 A033443

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved