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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.)