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A035082 Number of rooted polygonal cacti (Husimi graphs) with n nodes. 19

%I #17 Aug 30 2018 22:13:00

%S 0,1,0,1,1,3,5,13,27,67,157,390,963,2437,6186,15908,41127,107148,

%T 280569,738675,1953054,5185364,13816018,36934431,99030038,266254593,

%U 717652816,1938831589,5249221790,14240130827,38702218134,105367669062

%N Number of rooted polygonal cacti (Husimi graphs) with n nodes.

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

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

%H Andrew Howroyd, <a href="/A035082/b035082.txt">Table of n, a(n) for n = 0..500</a>

%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>

%H F. Harary and R. Z. Norman, <a href="http://www.jstor.org/stable/1969824">The Dissimilarity Characteristic of Husimi Trees</a>, Annals of Mathematics, 58 1953, pp. 134-141.

%H F. Harary and G. E. Uhlenbeck, <a href="http://www.pnas.org/content/39/4/315.full.pdf">On the Number of Husimi Trees</a>, Proc. Nat. Acad. Sci. USA vol. 39 pp. 315-322 1953

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%H <a href="/index/Ca#cacti">Index entries for sequences related to cacti</a>

%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>

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

%o (PARI)

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

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

%o 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

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

%K nonn,eigen

%O 0,6

%A _Christian G. Bower_, Nov 15 1998

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)