A005628 Number of chiral planted trees with n nodes. (Formerly M1641)

0, 0, 0, 0, 2, 6, 20, 60, 176, 510, 1484, 4314, 12624, 37126, 109864, 326958, 978528, 2943384, 8895792, 27001378, 82281216, 251636434, 772101086, 2376186784, 7333094178, 22688117658, 70360646672, 218678194238, 681016789056

Offset

0,5

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..28.

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(n) = A000625(n)-A005627(n) (given as g(n)=s(n)-p(n) on p. 357 of 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: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(s[n]-p[n], n=0..37); # here s[n]=A000625 and p[n]=A005627(n)

Mathematica

nmax = 28;
s[0] = s[1] = 1; s[_] = 0;
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, {n, 1, nmax}];
p[0] = 1;
Do[p[n+1] = Sum[s[k]*p[n-2*k], {k, 0, Floor[n/2]}], {n, 0, nmax}];
a[n_] := s[n] - p[n];
Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Jul 07 2024, after Maple code *)

Crossrefs

Cf. A000625, A005627.

Sequence in context: A082045 A358301 A361732 * A000620 A081251 A134293

Adjacent sequences: A005625 A005626 A005627 * A005629 A005630 A005631

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

More terms from Emeric Deutsch, May 16 2004

Status

approved