A001051 Number of subgroups of order n in orthogonal group O(3).

1, 3, 1, 5, 1, 5, 1, 7, 1, 5, 1, 8, 1, 5, 1, 7, 1, 5, 1, 7, 1, 5, 1, 10, 1, 5, 1, 7, 1, 5, 1, 7, 1, 5, 1, 7, 1, 5, 1, 7, 1, 5, 1, 7, 1, 5, 1, 8, 1, 5, 1, 7, 1, 5, 1, 7, 1, 5, 1, 8, 1, 5, 1, 7, 1, 5, 1, 7, 1, 5, 1, 7, 1, 5, 1, 7, 1, 5, 1, 7, 1, 5, 1, 7, 1, 5, 1, 7, 1, 5, 1, 7, 1, 5, 1, 7, 1, 5, 1, 7, 1, 5, 1, 7, 1, 5, 1, 7, 1, 5, 1, 7, 1, 5, 1, 7, 1, 5, 1, 8

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Orthogonal Group.

Formula

Has period 1 5 1 7 except that a(2) = 3, a(4) = 5, a(12) = 8, a(24) = 10, a(48) = a(60) = a(120) = 8.

Mathematica

a[2] = 3; a[4] = 5; a[12] = 8; a[24] = 10; a[48] = a[60] = a[120] = 8; a[n_] := Switch[Mod[n, 4], 0, 7, 1, 1, 2, 5, 3, 1]; Table[a[n], {n, 1, 96}] (* Jean-François Alcover, Oct 15 2013 *)

Prog

(PARI) A001051(n) = if((12==n)||(48==n)||(60==n)||(120==n), 8, if(24==n, 10, if((4==n)||(2==n), 1+n, [1, 5, 1, 7][1+((n-1)%4)]))); \\ Antti Karttunen, Jan 15 2019

Crossrefs

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

Sequence in context: A352453 A208239 A114567 * A214737 A348161 A334194

Adjacent sequences: A001048 A001049 A001050 * A001052 A001053 A001054

Keyword

nonn,easy,nice

Author

J. H. Conway

Extensions

Data section extended up to a(120) by Antti Karttunen, Jan 15 2019

Status

approved