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Search: id:A005629
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| A005629 |
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Number of achiral trees with n nodes.
(Formerly M0677)
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+0
2
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| 1, 1, 1, 2, 3, 5, 7, 14, 21, 40, 61, 118, 186, 355, 567, 1081, 1755, 3325, 5454, 10306, 17070, 32136, 53628, 100704, 169175, 316874, 535267, 1000524, 1698322, 3168500, 5400908, 10059823, 17211368, 32010736, 54947147, 102059572, 175702378
(list; graph; listen)
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OFFSET
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1,4
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REFERENCES
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R. W. Robinson, F. Harary and A. T. Balaban, Numbers of chiral and achiral alkanes..., Tetrahedron 32 (1976), 355-361.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Index entries for sequences related to trees
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FORMULA
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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 (deutsch(AT)duke.poly.edu), Nov 21 2004
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MAPLE
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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). (Deutsch)
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CROSSREFS
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Cf. A000625, A005627.
Sequence in context: A114625 A046808 A097799 this_sequence A028304 A157833 A151531
Adjacent sequences: A005626 A005627 A005628 this_sequence A005630 A005631 A005632
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Corrected and extended by Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 21 2004
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