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A001051 Number of subgroups of order n in orthogonal group O(3). 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A325249 A208239 A114567 * A214737 A046730 A002972

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

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Last modified May 26 02:35 EDT 2019. Contains 323579 sequences. (Running on oeis4.)