|
%I #9 May 25 2018 15:31:38
%S 1,2,7,15,44,107,295,763,2077,5533,15053,40697,111028,302583,828176,
%T 2267939,6225340,17103834,47062513,129616014,357364708,986110340,
%U 2723373330,7526669582,20816208417,57606623093,159514679011,441942381946,1225049208597,3397418545998
%N Number of fused bicyclic skeletons with n carbon atoms (see Parks et al. for precise definition).
%C 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
%H Andrew Howroyd, <a href="/A121165/b121165.txt">Table of n, a(n) for n = 4..200</a>
%H Camden A. Parks and James B. Hendrickson, <a href="https://doi.org/10.1021/ci00002a021">Enumeration of monocyclic and bicyclic carbon skeletons</a>, J. Chem. Inf. Comput. Sci., vol. 31, 334-339 (1991).
%o (PARI) \\ here G is A000598 as series
%o 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}
%o C1(n)={sum(k=1, n\2, d1^(2*k) + d2^k)/4}
%o C2(n)={sum(k=1, n\2, d2^k + d2^(k-k%2)*d1^(2*(k%2)))/4}
%o 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
%Y Cf. A125671.
%K nonn
%O 4,2
%A _Parthasarathy Nambi_, Aug 13 2006
%E More terms from _N. J. A. Sloane_, Aug 27 2006
%E Terms a(26) and beyond from _Andrew Howroyd_, May 25 2018
|
