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A182531
Extremal graph numbers for a triangle with an edge off it.
1
0, 1, 3, 4, 6, 9, 12, 16, 20, 25, 30, 36, 42, 49, 56, 64, 72, 81, 90, 100, 110, 121, 132, 144, 156, 169, 182, 196, 210, 225, 240, 256, 272
OFFSET
1,3
COMMENTS
The largest possible number of edges in a graph on n nodes that does not contain a triangle with an edge off it as a subgraph.
Assuming Colin Barker's conjectures this is A002378 and the positive terms of A000290 interleaved, except for a(3) = 3. - Omar E. Pol, Jan 25 2018
FORMULA
Conjectures from Colin Barker, Jul 04 2016: (Start)
a(n) = (-1+(-1)^n+2*n^2)/8 for n>3.
a(n) = n^2/4 for n>3 and even.
a(n) = (n^2-1)/4 for n>3 and odd.
a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n>4.
G.f.: x^2*(1+x-x^2)*(1-x^2+x^3) / ((1-x)^3*(1+x)).
(End)
EXAMPLE
For n=4 the 4-cycle is a graph on 4 nodes that avoids the triangle with an edge off it.
CROSSREFS
Sequence in context: A260109 A283777 A202171 * A097922 A103109 A241639
KEYWORD
nonn,more
AUTHOR
John Y. Kim, May 03 2012
EXTENSIONS
a(8)-a(23) from Paul Tabatabai, Jul 04 2016
a(24)-a(33) from Manfred Scheucher, Jan 25 2018
STATUS
approved