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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 (list; graph; refs; listen; history; text; internal format)
 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 Andrew Howroyd, Table of n, a(n) for n = 6..200 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 Cf. A121158, A125669. Sequence in context: A241527 A234387 A173867 * A146018 A145946 A109224 Adjacent sequences:  A121159 A121160 A121161 * A121163 A121164 A121165 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

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Last modified August 8 12:09 EDT 2022. Contains 356009 sequences. (Running on oeis4.)