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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 (list; graph; refs; listen; history; text; internal format)
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

Andrew Howroyd, Table of n, a(n) for n = 5..200

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

Cf. A107278, A121158, A121159, A121160.

Sequence in context: A073705 A355900 A328130 * A214650 A032772 A326232

Adjacent sequences:  A121155 A121156 A121157 * A121159 A121160 A121161

KEYWORD

nonn

AUTHOR

Parthasarathy Nambi, Aug 13 2006

EXTENSIONS

Terms a(26) and beyond from Andrew Howroyd, May 24 2018

STATUS

approved

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Last modified September 26 06:19 EDT 2022. Contains 356987 sequences. (Running on oeis4.)