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
Examples
a(23) = floor((23/5)^5) = floor(2059.62976) = 2059.
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.
Programs
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PARI
a(n)=n^5 \ 3125 \\ Charles R Greathouse IV, Oct 17 2016
Formula
a(n) = floor((n/5)^5).