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A121158
Number of spiro bicyclic skeletons with n carbon atoms (see Parks et al. for precise definition).
5
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
5,3
COMMENTS
Equivalently, the number of graphs on n unlabeled nodes with exactly 2 cycles of equal length joined at a single node and all nodes having degree at most 4. - Andrew Howroyd, May 24 2018
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
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}
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Parthasarathy Nambi, Aug 13 2006
EXTENSIONS
Terms a(26) and beyond from Andrew Howroyd, May 24 2018
STATUS
approved