|
| |
|
|
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
(list; graph; refs; listen; history; internal format)
|
|
|
|
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.
|
|
|
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
|
|
|
CROSSREFS
| Sequence in context: A176675 A115285 A004232 * A093523 A173247 A123386
Adjacent sequences: A140459 A140460 A140461 * A140463 A140464 A140465
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Jun 27 2008
|
| |
|
|
