OFFSET
0,5
COMMENTS
Conjecture 1.2, p. 2 of Frohmader.
REFERENCES
P. Turan, Research Problem, Kozl MTA Mat. Kutato Int. 6(1961)417-423.
LINKS
Nathaniel Johnston, Table of n, a(n) for n = 0..10000
Andrew Frohmader, More Constructions for Turan's (3, 4)-Conjecture
FORMULA
a(n) = (5/2)*(k^3) - (3/2)*(k^2) if n = 3*k; (5/2)*(k^3) + (k^2) - (1/2)*k if n = 3*k+1; (5/2)*(k^3) + (7/2)*(k^2) + k if n = 3*k+2.
Empirical g.f.: x^3*(x^3+2*x^2+x+1) / ((x-1)^4*(x^2+x+1)^2). - Colin Barker, May 04 2013
MAPLE
A140462 := proc(n) local k: k:=floor(n/3): if(n mod 3 = 0)then return 5*(k^3)/2 - 3*(k^2)/2: elif(n mod 3 = 1)then return 5*(k^3)/2 + k^2 - k/2: else return 5*(k^3)/2 + 7*(k^2)/2 + k: fi: end:
seq(A140462(n), n=0..40); # Nathaniel Johnston, Apr 26 2011
MATHEMATICA
a[n_] := Which[k = Floor[n/3]; Mod[n, 3] == 0, 5*(k^3)/2 - 3*(k^2)/2, Mod[n, 3] == 1, 5*(k^3)/2 + k^2 - k/2, True, 5*(k^3)/2 + 7*(k^2)/2 + k];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Nov 28 2017, from Maple *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jun 27 2008
STATUS
approved