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A121162
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Number of separated bicyclic skeletons with n carbon atoms (see Parks et al. for precise definition).
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3
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1, 3, 13, 41, 141, 440, 1391, 4244, 12913, 38651, 115082, 339646, 997709, 2915010, 8485573, 24612666, 71191458, 205393819, 591330506, 1699226719, 4874925420, 13965498369, 39957144189, 114193222891, 326023307022, 929958622555, 2650483647976, 7548608038736
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OFFSET
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6,2
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COMMENTS
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Equivalently, the number of connected graphs on n unlabeled nodes with exactly 2 cycles of equal length without any shared node and all nodes having degree at most 4. - Andrew Howroyd, May 25 2018
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 6..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).
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PROG
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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}
C1(n)={sum(k=1, n\4, d1^(4*k) + 2*d1^(2*k)*d2^k + d2^(2*k))*(1 + d1^2)/(8*(1-d1))}
C2(n)={sum(k=1, n\4, 2*(d2^(2*k) + d4^k)*(1 + d2))*(1+d1)/(8*(1-d2))}
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
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CROSSREFS
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Cf. A121158, A125669.
Sequence in context: A241527 A234387 A173867 * A146018 A145946 A109224
Adjacent sequences: A121159 A121160 A121161 * A121163 A121164 A121165
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KEYWORD
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nonn
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AUTHOR
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Parthasarathy Nambi, Aug 13 2006
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EXTENSIONS
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More terms from N. J. A. Sloane, Aug 27 2006
Terms a(26) and beyond from Andrew Howroyd, May 25 2018
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STATUS
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approved
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