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A035082 Number of rooted polygonal cacti (Husimi graphs) with n nodes. 19
0, 1, 0, 1, 1, 3, 5, 13, 27, 67, 157, 390, 963, 2437, 6186, 15908, 41127, 107148, 280569, 738675, 1953054, 5185364, 13816018, 36934431, 99030038, 266254593, 717652816, 1938831589, 5249221790, 14240130827, 38702218134, 105367669062 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

REFERENCES

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures.

F. Harary and E. M. Palmer, Graphical Enumeration, p. 71

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..500

C. G. Bower, Transforms (2)

F. Harary and R. Z. Norman, The Dissimilarity Characteristic of Husimi Trees, Annals of Mathematics, 58 1953, pp. 134-141.

F. Harary and G. E. Uhlenbeck, On the Number of Husimi Trees, Proc. Nat. Acad. Sci. USA vol. 39 pp. 315-322 1953

N. J. A. Sloane, Transforms

Index entries for sequences related to cacti

Index entries for sequences related to rooted trees

FORMULA

Shifts left under transform T where Ta = EULER(BIK(a)-a).

PROG

(PARI)

BIK(p)={(1/(1-p) + (1+p)/subst(1-p, x, x^2))/2}

EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}

seq(n)={my(p=O(x)); for(n=1, n, p=x+x^2*Ser(EulerT(Vec(BIK(p)-1)-Vec(p)))); concat([0], Vec(p))} \\ Andrew Howroyd, Aug 30 2018

CROSSREFS

Cf. A003080, A035083, A035084, A035085, A035086, A035087, A035088.

Sequence in context: A190570 A000631 A026569 * A005198 A160823 A077443

Adjacent sequences:  A035079 A035080 A035081 * A035083 A035084 A035085

KEYWORD

nonn,eigen

AUTHOR

Christian G. Bower, Nov 15 1998

STATUS

approved

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Last modified October 22 18:55 EDT 2018. Contains 316500 sequences. (Running on oeis4.)