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A003240
Number of partially achiral rooted trees.
(Formerly M1123)
1
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)
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 * A280543 A282566 A251706
KEYWORD
nonn,easy,changed
EXTENSIONS
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 26 2008
STATUS
approved