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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| 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 S. Plouffe in his 1992 dissertation, but this is incorrect.
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REFERENCES
| F. Harary and R. W. Robinson, The number of achiral trees, J. Reine Angew. Math., 278 (1975), 322-335.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 26 2008, Table of n, a(n) for n = 1..73
F. Harary and R. W. Robinson, The number of achiral trees, J. Reine Angew. Math., 278 (1975), 322-335.
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index entries for sequences related to trees
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PROG
| (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
| Sequence in context: A011962 A060172 A193196 * A055873 A185376 A191469
Adjacent sequences: A003240 A003241 A003242 * A003244 A003245 A003246
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 26 2008
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