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A003243 Number of partially achiral trees with n nodes.
(Formerly M0760)
1
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; text; internal format)
OFFSET

1,4

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 Simon Plouffe in his 1992 dissertation, but this is incorrect.

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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.

F. Harary and R. W. Robinson, The number of achiral trees, J. Reine Angew. Math., 278 (1975), 322-335. (Annotated scanned copy)

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

Index entries for sequences related to trees

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

CROSSREFS

Sequence in context: A060172 A193196 A319755 * A320160 A055873 A246565

Adjacent sequences:  A003240 A003241 A003242 * A003244 A003245 A003246

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 26 2008

STATUS

approved

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Last modified January 21 19:54 EST 2019. Contains 319350 sequences. (Running on oeis4.)