OFFSET
0,4
COMMENTS
Apart from the initial term this is the elliptic troublemaker sequence R_n(1,5) (also sequence R_n(4,5)) 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
R. L. Graham et al., eds., Handbook of Combinatorics, Vol. 2, p. 1234.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..10000
Kevin Beanland, Hung Viet Chu, and Carrie E. Finch-Smith, Generalized Schreier sets, linear recurrence relation, Turán graphs, arXiv:2112.14905 [math.CO], 2021.
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
Wikipedia, Turán graph
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,1,-2,1).
FORMULA
G.f.: (x^5+x^4+x^3+x^2)/((1-x^5)*(1-x)^2).
a(n) = Sum_{k=0..n} A011558(k)*(n-k). - Reinhard Zumkeller, Nov 30 2009
a(n) = floor( 2n^2/5 ). - Wesley Ivan Hurt, Jun 20 2013
a(n) = Sum_{i=1..n} floor(4*i/5). - Wesley Ivan Hurt, Sep 12 2017
MATHEMATICA
Table[Floor[2n^2/5], {n, 0, 60}]
PROG
(Magma) [2*n^2 div 5: n in [0..60]]; // Vincenzo Librandi, Apr 20 2015
(PARI) a(n)=2*n^2\5 \\ Charles R Greathouse IV, Apr 20 2015
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
STATUS
approved