A121158 Number of spiro bicyclic skeletons with n carbon atoms (see Parks et al. for precise definition).
1, 1, 5, 10, 34, 82, 240, 630, 1764, 4752, 13108, 35703, 98108, 268553, 737864, 2025779, 5572160, 15331017, 42230755, 116395955, 321089489, 886320404, 2448312482, 6767186801, 18716207007, 51792971141, 143403624284, 397254931272, 1101003729796, 3052855074597
Offset: 5
Keywords
References
- Camden A. Parks and James B. Hendrickson, Enumeration of monocyclic and bicyclic carbon skeletons, J. Chem. Inf. Comput. Sci., vol. 31, 334-339 (1991).
Links
- Andrew Howroyd, Table of n, a(n) for n = 5..200
Programs
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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} CycleIndex(n)={sum(k=1, (n-1)\4, (j1^(4*k) + 2*j1^(2*k)*j2^k + j2^(2*k))*(1 + j1^2) + 2*(j2^(2*k) + j4^k)*(1 + j2))/8} seq(n)={my(t=G(n)); t=x*(t^2+subst(t, x, x^2))/2; my(g(e)=subst(t + O(x*x^(n\e)), x, x^e) + O(x^n)); Vec(substvec(CycleIndex(n), [j1,j2,j4], [g(1),g(2),g(4)]))} \\ Andrew Howroyd, May 24 2018
Extensions
Terms a(26) and beyond from Andrew Howroyd, May 24 2018
Comments