A051881 Number of subgroups of order n in special orthogonal group SO(3).

1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..12000

Formula

Has period 1, 2 except for a(2) = 1, a(12) = a(24) = a(60) = 3.

Example

The groups are "nn", of order n; "22n", of order 2n; "332", "432", "532" of orders 12,24,60.

Mathematica

a[2] = 1; a[12|24|60] = 3; a[n_] := 2-Mod[n, 2]; Array[a, 105] (* Jean-François Alcover, Nov 12 2015 *)

Prog

(PARI) a(n)=if(n==2||n==12||n==24||n==60, if(n>2, 3, 1), if(n%2, 1, 2)) \\ Charles R Greathouse IV, Nov 10 2015

Crossrefs

The main sequences concerned with group theory are A000001, A000679, A001034, A001051, A001228, A005180, A000019, A000637, A000638, A002106, A005432, A051881.

Sequence in context: A160979 A323287 A167679 * A363852 A357859 A338731

Adjacent sequences: A051878 A051879 A051880 * A051882 A051883 A051884

Keyword

nonn,easy,nice

Author

J. H. Conway

Extensions

More terms from James A. Sellers and David W. Wilson Dec 16 1999

Status

approved