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
Links
- Antti Karttunen, Table of n, a(n) for n = 1..10000
- Eric Weisstein's World of Mathematics, Orthogonal Group.
Crossrefs
Programs
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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 *) -
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
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.
Extensions
Data section extended up to a(120) by Antti Karttunen, Jan 15 2019