A182079 a(n) = floor(n*floor((n-1)/2)/3).

0, 0, 0, 1, 1, 3, 4, 7, 8, 12, 13, 18, 20, 26, 28, 35, 37, 45, 48, 57, 60, 70, 73, 84, 88, 100, 104, 117, 121, 135, 140, 155, 160, 176, 181, 198, 204, 222, 228, 247, 253, 273, 280, 301, 308, 330, 337, 360, 368, 392, 400, 425, 433, 459, 468, 495, 504, 532, 541, 570, 580, 610, 620, 651, 661, 693, 704, 737, 748, 782, 793, 828, 840, 876, 888, 925, 937, 975, 988

Offset: 0

Author

N. J. A. Sloane, Apr 10 2012

Keywords

• nonn
• easy

Comments

Maximal number of edge-disjoint cycles of complete graph on n nodes.

References

• J.-C. Bermond, The circuit-hypergraph of a tournament. Infinite and finite sets (Colloq., Keszthely, 1973; dedicated to P. Erdős on his 60th birthday), Vol. I, pp. 165--180. Colloq. Math. Soc. Janos Bolyai, Vol. 10, North-Holland, Amsterdam, 1975. MR0396319 (53 #187)

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Gary Chartrand, Dennis Gellere, and Stephen Hedetniemi, Graphs with forbidden subgraphs, J. Combinatorial Theory Ser. B 10 1971 12--41. MR0285427 (44 #2645).
• Jannik Dreier, Jean-Guillaume Dumas, Pascal Lafourcade, and Léo Robert, Optimal Threshold Padlock Systems, arXiv:2004.11552 [cs.CR], 2020. See also hal-02552281, 2020.
• Sela Fried, On A182079, 2024.
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,0,1,-1,-1,1).

Crossrefs

This is a lower bound on A003141. [Bermond]

Programs

Mathematica

Table[Floor[(n/3)*Floor[(n - 1)/2]], {n, 0, 50}] (* G. C. Greubel, Aug 20 2017 *)

PARI

a(n) = n*((n-1)\2)\3 \\ G. C. Greubel, Aug 20 2017

Formula

Empirical g.f.: x^3*(x^4+x^3+x^2+1)/((1-x)^3*(1+x)^2*(x^2-x+1)*(x^2+x+1) ). - Colin Barker, Nov 18 2012

The conjectured g.f. is correct. See links. - Sela Fried, Dec 27 2024