OFFSET
0,4
COMMENTS
Apart from the initial term this is the elliptic troublemaker sequence R_n(1,7) (also sequence R_n(6,7)) in the notation of Stange (see Table 1, p.16). For other elliptic troublemaker sequences R_n(a,b) see the cross references below. - Peter Bala, Aug 12 2013
REFERENCES
Graham et al., Handbook of Combinatorics, Vol. 2, p. 1234.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
K. E. Stange, Integral points on elliptic curves and explicit valuations of division polynomials, arXiv:1108.3051 [math.NT], 2011-2014.
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,-1,0,0,0,0,1,-2,1).
FORMULA
a(n) = Sum_{k=0..n} A109720(k)*(n-k). [Reinhard Zumkeller, Nov 30 2009]
G.f.: -x^2*(x+1)*(x^2-x+1)*(x^2+x+1)/((x-1)^3*(x^6+x^5+x^4+x^3+x^2+x+1)). [Colin Barker, Aug 09 2012]
a(n) = floor(3*n^2/7). - Peter Bala, Aug 12 2013
a(0)=0, a(1)=0, a(2)=1, a(3)=3, a(4)=6, a(5)=10, a(6)=15, a(7)=21, a(8)=27, a(n)=2*a(n-1)-a(n-2)+a(n-7)-2*a(n-8)+a(n-9). - Harvey P. Dale, Mar 19 2015
a(n) = Sum_{i=1..n} floor(6*i/7). - Wesley Ivan Hurt, Sep 12 2017
MATHEMATICA
CoefficientList[Series[- x^2 (x + 1) (x^2 - x + 1) (x^2 + x + 1)/((x - 1)^3 (x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)), {x, 0, 60}], x] (* Vincenzo Librandi, Oct 19 2013 *)
LinearRecurrence[{2, -1, 0, 0, 0, 0, 1, -2, 1}, {0, 0, 1, 3, 6, 10, 15, 21, 27}, 60] (* Harvey P. Dale, Mar 19 2015 *)
PROG
(Magma) [Floor(3*n^2/7): n in [0..60]]; // Vincenzo Librandi, Oct 19 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Oct 19 2013
STATUS
approved