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%I M0677 #30 Dec 06 2020 08:31:11
%S 1,1,1,2,3,5,7,14,21,40,61,118,186,355,567,1081,1755,3325,5454,10306,
%T 17070,32136,53628,100704,169175,316874,535267,1000524,1698322,
%U 3168500,5400908,10059823,17211368,32010736,54947147,102059572,175702378
%N Number of achiral trees with n nodes.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H L. Bytautats and D. J. Klein, <a href="https://doi.org/10.1021/ci990021g">Alkane Isomere Combinatorics: Stereostructure enumeration and graph-invariant and molecylar-property distributions</a>, J. Chem. Inf. Comput. Sci 39 (1999) 803, Table 1.
%H R. W. Robinson, F. Harary and A. T. Balaban, <a href="http://dx.doi.org/10.1016/0040-4020(76)80049-X">The numbers of chiral and achiral alkanes and monosubstituted alkanes</a>, Tetrahedron 32 (1976), 355-361.
%H R. W. Robinson, F. Harary and A. T. Balaban, <a href="/A000625/a000625.pdf">Numbers of chiral and achiral alkanes and monosubstituted alkanes</a>, Tetrahedron 32 (3) (1976), 355-361. (Annotated scanned copy)
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F a(n+1) = (p(n+1)+s((n+1)/2)+s(n/4))/2, where p(n)=A005627(n) and s(n)=A000625(n) (eq. (23) in the Robinson et al. reference). - _Emeric Deutsch_, Nov 21 2004
%p s[0]:=1:s[1]:=1:for n from 0 to 60 do s[n+1/3]:=0 od:for n from 0 to 60 do s[n+2/3]:=0 od:for n from 1 to 55 do s[n+1]:=(2*n/3*s[n/3]+sum(j*s[j]*sum(s[k]*s[n-j-k],k=0..n-j),j=1..n))/n od: p[0]:=1: for n from 0 to 50 do > p[n+1]:=sum(s[k]*p[n-2*k],k=0..floor(n/2)) od:seq(p[j],j=0..45): P:=proc(n) if floor(n)=n then p[n] else 0 fi end:S:=proc(n) if floor(n)=n then s[n] else 0 fi end:t:=n->(P(n)+S(n/2)+S((n-1)/4))/2: seq(t(n),n=1..40); # here s[n]=A000625(n), p[n]=A005627(n). - _Emeric Deutsch_
%Y Cf. A000625, A005627.
%K nonn
%O 1,4
%A _N. J. A. Sloane_
%E Corrected and extended by _Emeric Deutsch_, Nov 21 2004
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