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A121162
Number of separated bicyclic skeletons with n carbon atoms (see Parks et al. for precise definition).
3
1, 3, 13, 41, 141, 440, 1391, 4244, 12913, 38651, 115082, 339646, 997709, 2915010, 8485573, 24612666, 71191458, 205393819, 591330506, 1699226719, 4874925420, 13965498369, 39957144189, 114193222891, 326023307022, 929958622555, 2650483647976, 7548608038736
OFFSET
6,2
COMMENTS
Equivalently, the number of connected graphs on n unlabeled nodes with exactly 2 cycles of equal length without any shared node and all nodes having degree at most 4. - Andrew Howroyd, May 25 2018
LINKS
Camden A. Parks and James B. Hendrickson, Enumeration of monocyclic and bicyclic carbon skeletons, J. Chem. Inf. Comput. Sci., vol. 31, 334-339 (1991).
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)={sum(k=1, n\4, d1^(4*k) + 2*d1^(2*k)*d2^k + d2^(2*k))*(1 + d1^2)/(8*(1-d1))}
C2(n)={sum(k=1, n\4, 2*(d2^(2*k) + d4^k)*(1 + d2))*(1+d1)/(8*(1-d2))}
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], [g(d, 1), g(d, 2)]) + g(s, 2)*substvec(C2(n-2), [d1, d2, d4], [g(d, 1), g(d, 2), g(d, 4)]))} \\ Andrew Howroyd, May 25 2018
CROSSREFS
Sequence in context: A241527 A234387 A173867 * A146018 A145946 A109224
KEYWORD
nonn
AUTHOR
Parthasarathy Nambi, Aug 13 2006
EXTENSIONS
More terms from N. J. A. Sloane, Aug 27 2006
Terms a(26) and beyond from Andrew Howroyd, May 25 2018
STATUS
approved