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A121162 Number of separated bicyclic skeletons with n carbon atoms (see Parks et al. for precise definition). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,2

COMMENTS

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

LINKS

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).

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}

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

CROSSREFS

Cf. A121158, A125669.

Sequence in context: A241527 A234387 A173867 * A146018 A145946 A109224

Adjacent sequences:  A121159 A121160 A121161 * A121163 A121164 A121165

KEYWORD

nonn

AUTHOR

Parthasarathy Nambi, Aug 13 2006

EXTENSIONS

More terms from N. J. A. Sloane, Aug 27 2006

Terms a(26) and beyond from Andrew Howroyd, May 25 2018

STATUS

approved

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Last modified August 8 12:09 EDT 2022. Contains 356009 sequences. (Running on oeis4.)