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A208647 Numerators of Pokrovskiy's lower bound on the ratio of e(G^n) the number of edges in the n-th power of a graph G, to E(G) the number of edges of G. 1
1, 1, 1, 7, 2, 2, 17, 3, 3, 31, 4, 4, 49, 5, 5, 71 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Denominators are A208648. 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. A208648.

Sequence in context: A334961 A154759 A300304 * A163981 A126341 A324788

Adjacent sequences:  A208644 A208645 A208646 * A208648 A208649 A208650

KEYWORD

nonn,easy,frac

AUTHOR

Jonathan Vos Post, Feb 29 2012

STATUS

approved

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Last modified July 4 15:25 EDT 2020. Contains 335448 sequences. (Running on oeis4.)