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A140462
Turan's upper bound on the number of triangles of a simplicial complex of dimension two for which every minimal non-face has three vertices.
1
0, 0, 0, 1, 3, 7, 14, 23, 36, 54, 75, 102, 136, 174, 220, 275, 335, 405, 486, 573, 672, 784, 903, 1036, 1184, 1340, 1512, 1701, 1899, 2115, 2350, 2595, 2860, 3146, 3443, 3762, 4104, 4458, 4836, 5239, 5655, 6097, 6566, 7049, 7560, 8100, 8655
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.
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
Sequence in context: A294400 A115285 A004232 * A227841 A225256 A093523
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jun 27 2008
STATUS
approved