|
Search: id:A003243
|
|
|
| A003243 |
|
Number of partially achiral trees with n nodes.
(Formerly M0760)
|
|
+0
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; listen)
|
|
|
OFFSET
|
1,4
|
|
|
REFERENCES
|
F. Harary and R. W. Robinson, The number of achiral trees, J. Reine Angew. Math., 278 (1975), 322-335.
|
|
LINKS
|
Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 26 2008, Table of n, a(n) for n = 1..73
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
F. Harary and R. W. Robinson, The number of achiral trees, J. Reine Angew. Math., 278 (1975), 322-335.
|
|
FORMULA
|
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.
|
|
PROGRAM
|
(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
|
Adjacent sequences: A003240 A003241 A003242 this_sequence A003244 A003245 A003246
Sequence in context: A018741 A011962 A060172 this_sequence A055873 A091053 A095064
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
njas
|
|
EXTENSIONS
|
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 26 2008
|
|
|
Search completed in 0.002 seconds
|
