A185721 Arises in the maximum number of C5's in a triangle-free graph.

0, 0, 0, 0, 0, 1, 2, 5, 10, 18, 32, 51, 79, 118, 172, 243, 335, 454, 604, 792, 1024, 1306, 1649, 2059, 2548, 3125, 3802, 4591, 5507, 6563, 7776, 9161, 10737, 12523, 14539, 16807, 19349, 22190, 25355, 28871, 32768, 37073, 41821, 47042, 52773, 59049, 65908, 73390

Offset

0,7

Links

Nathaniel Johnston, Table of n, a(n) for n = 0..1000

P. Erdős, On some problems in graph theory, combinatorial analysis and combinatorial number theory, Graph Theory and Combinatorics, Proc. Conf. Hon. P. Erdos, Cambridge 1983, 1-17 (1984).

Andrzej Grzesik, On the maximum number of C5's in a triangle-free graph, arXiv:1102.0962 [math.CO], 2011-2012.

E. Győri, On the number of C5s in a triangle-free graph, Combinatorica 9(1) (1989) 101-102.

H. Hatami, J. Hladky, D. Král, S. Norine, and A. Razborov, On the Number of Pentagons in Triangle-Free Graphs, arXiv:1102.1634 [math.CO], 2011-2012.

Formula

a(n) = floor((n/5)^5).

Example

a(23) = floor((23/5)^5) = floor(2059.62976) = 2059.

Prog

(PARI) a(n)=n^5 \ 3125 \\ Charles R Greathouse IV, Oct 17 2016

Crossrefs

Sequence in context: A298107 A034350 A006327 * A304796 A103577 A326508

Adjacent sequences: A185718 A185719 A185720 * A185722 A185723 A185724

Keyword

nonn,easy

Author

Jonathan Vos Post, Feb 10 2011

Status

approved