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 A005627 Number of achiral planted trees with n nodes. (Formerly M0698) 2
 1, 1, 1, 2, 3, 5, 8, 14, 23, 41, 69, 122, 208, 370, 636, 1134, 1963, 3505, 6099, 10908, 19059, 34129, 59836, 107256, 188576, 338322, 596252, 1070534, 1890548, 3396570, 6008908, 10801816, 19139155, 34422537, 61074583, 109894294, 195217253 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS R. W. Robinson, F. Harary and A. T. Balaban, The numbers of chiral and achiral alkanes and monosubstituted alkanes, Tetrahedron 32 (1976), 355-361. R. W. Robinson, F. Harary and A. T. Balaban, Numbers of chiral and achiral alkanes and monosubstituted alkanes, Tetrahedron 32 (3) (1976), 355-361. (Annotated scanned copy) FORMULA a(0)=1, a(n+1):=sum(s(k)*a(n-2*k), k=0..floor(n/2)) (n>=0), where s(n)=A000625(n) (this is eq. (15) in the Robinson et al. paper). - Emeric Deutsch, May 16 2004 MAPLE s:=1:s:=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:a:=1: for n from 0 to 50 do a[n+1]:=sum(s[k]*a[n-2*k], k=0..floor(n/2)) od:seq(a[j], j=0..45); # here s[n]=A000625(n). CROSSREFS Cf. A000625. Sequence in context: A318520 A039828 A246360 * A191794 A191388 A194850 Adjacent sequences:  A005624 A005625 A005626 * A005628 A005629 A005630 KEYWORD nonn AUTHOR EXTENSIONS More terms from Emeric Deutsch, May 16 2004 STATUS approved

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Last modified November 14 04:56 EST 2019. Contains 329110 sequences. (Running on oeis4.)