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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
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
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
KEYWORD
nonn,easy,frac
AUTHOR
Jonathan Vos Post, Feb 29 2012
STATUS
approved