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A003241 Number of achiral rooted trees.
(Formerly M1101)
1
1, 1, 2, 4, 8, 15, 26, 45, 71, 110, 168, 247, 351, 503, 700, 944, 1294, 1719, 2267, 2961, 3839, 4891, 6297, 7891, 9912, 12347, 15381, 18784, 23203, 28138, 34233, 41275, 49824, 59306, 71309, 84268, 100127, 118045, 139472, 162659 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

There may be an error in eq (37) in the Harary-Robinson paper. - R. J. Mathar, Sep 28 2011

REFERENCES

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

LINKS

Table of n, a(n) for n=1..40.

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)

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

MAPLE

L := BFILETOLIST("b003238.txt") ;

Pofxn := proc(n)

        global L;

        add( op(i, L)*x^(i+1), i=1..120) ;

        subs(x=x^n, %) ;

end proc:

P := Pofxn(1) ;

Rn := proc(n)

        global L;

        (Pofxn(n-2)*Pofxn(2)+Pofxn(n-1)*Pofxn(1)-Pofxn(n))/x^(n-1) ;

end proc:

Px2 := Pofxn(2) ;

Px3 := Pofxn(3) ;

Px4 := Pofxn(4) ;

# eq (37) seems not to work

# R := 2*x+P^2/x^2+(1-x)*P/x*(Px2/x^2-1)-(P^2-Px2)/2/x -Px3/x^2-(Px2^2-Px4)/2/x^3 ;

#use eqs (39)-(44) instead

R := x+P+(P^2+Px2)/2/x+P*Px2/x^2+P*Px3/x^3+(Px2^2-Px4)/2/x^3 :

# heuristics, adding up to R^(40) suffices for first 80 terms

for n from 5 to 40 do

        R := R+Rn(n) :

end do:

taylor(R, x=0, 80) ;

gfun[seriestolist](%) ; # R. J. Mathar, Sep 28 2011

CROSSREFS

Sequence in context: A187154 A179001 A222147 * A279320 A182844 A191630

Adjacent sequences:  A003238 A003239 A003240 * A003242 A003243 A003244

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Extended by R. J. Mathar, Sep 28 2011

STATUS

approved

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Last modified November 19 07:02 EST 2017. Contains 294915 sequences.