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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

Table of n, a(n) for n=0..36.

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)

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

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[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:a[0]:=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

N. J. A. Sloane.

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.)