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A003243
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Number of partially achiral trees with n nodes.
(Formerly M0760)
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1
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1, 1, 1, 2, 3, 6, 9, 19, 30, 61, 99, 198, 333, 650, 1115, 2143, 3743, 7101, 12553, 23605, 42115, 78670, 141284, 262679, 474083, 878386, 1591038, 2940512, 5340712, 9852201, 17930619, 33031498, 60209609, 110801271, 202208576, 371820314
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OFFSET
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1,4
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COMMENTS
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The g.f. (1-z**2-2*z**3-8*z**4+7*z**5+4*z**6)/(1-z-z**2-2*z**3-6*z**4+14*z**5) was conjectured by Simon Plouffe in his 1992 dissertation, but this is incorrect.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) ~ c * d^n, where d = 1.8332964415228533737988849634129366404833316666328290543862325494628120733... is the root of the equation Sum_{k>=1} A000081(k) / d^(2*k-1) = 1 and c = 0.123308773712306885475561730669251048497115967922743533462465528423705228... - Vaclav Kotesovec, Dec 13 2020
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PROG
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(PARI) t(n)=local(A=x); if(n<1, 0, for(k=1, n-1, A/=(1-x^k+x*O(x^n))^polcoeff(A, k)); polcoeff(A, n)) {n=100; Ty2=sum(i=0, n, t(i)*y^(2*i)); p=subst(y*Ty2/(y-Ty2), y, y+y*O(y^n)); p=Pol(p, y); a=subst(Ty2*(y+p+(p^2-subst(p, y, y^2))/(2*y))/y^2-(p^2+subst(p, y, y^2))/(2*y^2)+Ty2, y, x+x*O(x^n)); for(i=0, n-2, print1(polcoeff(a, i)", "))} \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 26 2008
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 26 2008
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STATUS
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approved
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