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A185721
Arises in the maximum number of C5's in a triangle-free graph.
2
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
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
KEYWORD
nonn,easy
AUTHOR
Jonathan Vos Post, Feb 10 2011
STATUS
approved