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%I #18 Jul 03 2018 02:42:20
%S 1,1,4,8,24,55,147,365,954,2431,6327,16369,42743,111595,292849,769805,
%T 2030456,5366844,14222475,37768154,100510364,267987501,715847932,
%U 1915406263,5133382014,13778469949,37035674682,99683747508,268647638770,724879674667,1958151665752
%N Number of monocyclic skeletons with n carbon atoms and a ring size of 4.
%H Andrew Howroyd, <a href="/A116719/b116719.txt">Table of n, a(n) for n = 4..200</a>
%H Camden A. Parks and James B. Hendrickson, <a href="https://pubs.acs.org/doi/abs/10.1021/ci00002a021">Enumeration of monocyclic and bicyclic carbon skeletons</a>, J. Chem. Inf. Comput. Sci., vol. 31, 334-339 (1991).
%e If n=5 then the number of monocyclic skeletons with ring size of four is 1.
%t G[n_] := Module[{g}, Do[g[x_] = 1 + x*(g[x]^3/6 + g[x^2]*g[x]/2 + g[x^3]/3) + O[x]^n // Normal, {n}]; g[x]];
%t T[n_, k_] := Module[{t = G[n], g}, t = x*((t^2 + (t /. x -> x^2))/2); g[e_] = (Normal[t + O[x]^Quotient[n, e]] /. x -> x^e) + O[x]^n // Normal; Coefficient[(Sum[EulerPhi[d]*g[d]^(k/d), {d, Divisors[k]}]/k + If[OddQ[ k], g[1]*g[2]^Quotient[k, 2], (g[1]^2 + g[2])*g[2]^(k/2-1)/2])/2, x, n]];
%t a[n_] := T[n, 4];
%t Table[a[n], {n, 4, 30}] (* _Jean-François Alcover_, Jul 03 2018, after _Andrew Howroyd_ *)
%Y Column k=4 of A305059.
%Y Cf. A063832.
%K nonn
%O 4,3
%A _Parthasarathy Nambi_, Aug 13 2006
%E More terms from _N. J. A. Sloane_, Aug 27 2006
%E a(5) corrected and terms a(26) and beyond from _Andrew Howroyd_, May 24 2018
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