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 A121165 Number of fused bicyclic skeletons with n carbon atoms (see Parks et al. for precise definition). 3
 1, 2, 7, 15, 44, 107, 295, 763, 2077, 5533, 15053, 40697, 111028, 302583, 828176, 2267939, 6225340, 17103834, 47062513, 129616014, 357364708, 986110340, 2723373330, 7526669582, 20816208417, 57606623093, 159514679011, 441942381946, 1225049208597, 3397418545998 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,2 COMMENTS Equivalently, the number of connected graphs on n unlabeled nodes with exactly 2 cycles of the same length joined at a single edge and all nodes having degree at most 4. - Andrew Howroyd, May 25 2018 LINKS Andrew Howroyd, Table of n, a(n) for n = 4..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\2, d1^(2*k) + d2^k)/4} C2(n)={sum(k=1, n\2, d2^k + d2^(k-k%2)*d1^(2*(k%2)))/4} 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. A125671. Sequence in context: A052130 A065506 A330454 * A093652 A200862 A096690 Adjacent sequences:  A121162 A121163 A121164 * A121166 A121167 A121168 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 13 10:40 EDT 2022. Contains 356080 sequences. (Running on oeis4.)