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 A035085 Number of polygonal cacti (Husimi graphs) with n nodes. 4
 1, 1, 0, 1, 1, 2, 2, 5, 7, 16, 28, 63, 131, 301, 673, 1600, 3773, 9158, 22319, 55255, 137563, 345930, 874736, 2227371, 5700069, 14664077, 37888336, 98310195, 256037795, 669184336, 1754609183, 4614527680 (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, Camb. 1998, p. 301. F. Harary and E. M. Palmer, Graphical Enumeration, p. 71 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 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..500 FORMULA G.f.: A(x) = B(x) + C(x) - B(x)*D(x) where B, C, D are gfs of A035082, A035083, A035084. PROG (PARI) BIK(p)={(1/(1-p) + (1+p)/subst(1-p, x, x^2))/2} DIK(p, n)={(sum(d=1, n, eulerphi(d)/d*log(subst(1/(1+O(x*x^(n\d))-p), x, x^d))) + ((1+p)^2/(1-subst(p, x, x^2))-1)/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)))); Vec(1 + DIK(p, n) - (p^2 + subst(p, x, x^2))/2 - p*(BIK(p)-1-p))} \\ Andrew Howroyd, Aug 31 2018 CROSSREFS Cf. A035082, A035083, A035084. Sequence in context: A047083 A238422 A327019 * A208238 A127413 A145344 Adjacent sequences:  A035082 A035083 A035084 * A035086 A035087 A035088 KEYWORD nonn AUTHOR Christian G. Bower, Nov 15 1998 EXTENSIONS Terms a(32) and beyond from Andrew Howroyd, Aug 31 2018 STATUS approved

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Last modified December 6 04:14 EST 2019. Contains 329784 sequences. (Running on oeis4.)