%I #42 Jul 14 2022 09:30:51

%S 0,0,0,0,0,1,2,5,10,18,32,51,79,118,172,243,335,454,604,792,1024,1306,

%T 1649,2059,2548,3125,3802,4591,5507,6563,7776,9161,10737,12523,14539,

%U 16807,19349,22190,25355,28871,32768,37073,41821,47042,52773,59049,65908,73390

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

%H Nathaniel Johnston, <a href="/A185721/b185721.txt">Table of n, a(n) for n = 0..1000</a>

%H P. Erdős, <a href="https://users.renyi.hu/~p_erdos/1984-11.pdf">On some problems in graph theory, combinatorial analysis and combinatorial number theory</a>, Graph Theory and Combinatorics, Proc. Conf. Hon. P. Erdos, Cambridge 1983, 1-17 (1984).

%H Andrzej Grzesik, <a href="http://arxiv.org/abs/1102.0962">On the maximum number of C5's in a triangle-free graph</a>, arXiv:1102.0962 [math.CO], 2011-2012.

%H E. Győri, <a href="https://doi.org/10.1007/BF02122689">On the number of C5s in a triangle-free graph</a>, Combinatorica 9(1) (1989) 101-102.

%H H. Hatami, J. Hladky, D. Král, S. Norine, and A. Razborov, <a href="http://arxiv.org/abs/1102.1634">On the Number of Pentagons in Triangle-Free Graphs</a>, arXiv:1102.1634 [math.CO], 2011-2012.

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

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

%o (PARI) a(n)=n^5 \ 3125 \\ _Charles R Greathouse IV_, Oct 17 2016

%K nonn,easy

%O 0,7

%A _Jonathan Vos Post_, Feb 10 2011