A121165 Number of fused bicyclic skeletons with n carbon atoms (see Parks et al. for precise definition).

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

Offset: 4

Author

Parthasarathy Nambi, Aug 13 2006

Keywords

• nonn

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).

Crossrefs

Cf. A125671.

Programs

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

Extensions

More terms from N. J. A. Sloane, Aug 27 2006

Terms a(26) and beyond from Andrew Howroyd, May 25 2018