

A208648


Denominators of Pokrovskiy's lower bound on the ratio of e(G^n) the number of edges in the nth power of a graph G, to E(G) the number of edges of G.


1



2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1, 10, 1, 1, 12
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OFFSET

0,1


COMMENTS

Numerators are A208647. The fractions begin: 1/2, 1/2, 7/4, 2/1, 2/1, 17/6, 3/1, 3/1, 31/8, 4/1, 4/1, 49/10, 5/1, 5/1, 71/12.


LINKS

Table of n, a(n) for n=0..15.
Alexey Pokrovskiy, Edge growth in graph powers, arXiv:1202.6085v1 [math.CO], Feb 27, 2012.


FORMULA

If n == 0 (mod 3) then e(G^n)/e(G) = ((n+3)/3)  3/(2*(n+3));
If n =/= 0 (mod 3) then e(G^n)/e(G) = ceiling(n/3).


CROSSREFS

Cf. A003417 (continued fraction for e), A208647.
Sequence in context: A061462 A294334 A122578 * A005131 A105477 A325772
Adjacent sequences: A208645 A208646 A208647 * A208649 A208650 A208651


KEYWORD

nonn,easy,frac


AUTHOR

Jonathan Vos Post, Feb 29 2012


STATUS

approved



