OFFSET
5,2
COMMENTS
The resulting graph will actually have three cycles. See A121331 for the special case of all three cycles having the same length.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 5..200
EXAMPLE
Illustration of graphs for n=5 and n=6:
o o--o o o--o
/|\ /|\ /|\ /| |
o o o o o o o o o--o o o |
\|/ \|/ \|/ \| |
o o o o--o
PROG
(PARI) \\ here G is A000598 as series
G(n)={my(g=O(x)); for(n=1, n, g = 1 + x*(g^3/6 + subst(g, x, x^2)*g/2 + subst(g, x, x^3)/3) + O(x^n)); g}
C1(n)={subst(Pol(x^3*d1^3/(1-x*d1)^3 + 3*x^3*d1*d2/((1-x*d1)*(1-x^2*d2)) + 2*x^3*d3/(1-x^3*d3) + O(x*x^n)), x, 1)/12}
C2(n)={subst(Pol(((x*d1+x^2*d2)/(1-x^2*d2))^3 + 3*(x*d1+x^2*d2)*x^2*d2/(1-x^2*d2)^2 + 2*(x^3*d3 + x^6*d6)/(1-x^6*d6) + O(x*x^n)), x, 1)/12}
seq(n)={my(s=G(n)); my(d=x*(s^2+subst(s, x, x^2))/2); my(g(p, e)=subst(p + O(x*x^(n\e)), x, x^e)); Vec(O(x^n/x) + g(s, 1)^2*substvec(C1(n-2), [d1, d2, d3], [g(d, 1), g(d, 2), g(d, 3)]) + g(s, 2)*substvec(C2(n-2), [d1, d2, d3, d6], [g(d, 1), g(d, 2), g(d, 3), g(d, 6)]))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, May 26 2018
STATUS
approved