A003240 Number of partially achiral rooted trees. (Formerly M1123)

1, 1, 2, 4, 8, 16, 31, 62, 120, 236, 454, 884, 1697, 3275, 6266, 12020, 22935, 43788, 83325, 158516, 300914, 570794, 1081157, 2045934, 3867617, 7304149, 13783221, 25984936, 48956715, 92155376, 173376484, 325919786, 612378787, 1149777034

Offset

1,3

References

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

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..3760 (terms 1..70 from Herman Jamke)

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

Formula

a(n) ~ c * d^n * n, where d = 1.8332964415228533737988849634129366404833316666328290543862325494628120733... is the root of the equation Sum_{k>=1} A000081(k) / d^(2*k-1) = 1 and c = 0.030410107348865811204534352170117292921782094079168428605205142049899... - Vaclav Kotesovec, Dec 13 2020

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, 100, t(i)*y^(2*i)); p=subst(y*Ty2/(y-Ty2), y, y+y*O(y^n)); p=Pol(p, y); r=subst(Ty2*(y+p+(p^2-subst(p, y, y^2))/(2*y))/y^2, y, x+x*O(x^n)); for(I=1, n-2, print1(polcoeff(r, i)", "))} \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 26 2008

Crossrefs

Sequence in context: A239557 A001591 A194628 * A378698 A280543 A282566

Adjacent sequences: A003237 A003238 A003239 * A003241 A003242 A003243

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved