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A182039 Number of orthogonal 2 x 2 matrices over the ring Z/nZ. 1
0, 2, 8, 16, 8, 16, 16, 64, 24, 16, 24, 128, 24, 32, 64, 128, 32, 48, 40, 128, 128, 48, 48, 512, 40, 48, 72, 256, 56, 128, 64, 256, 192, 64, 128, 384, 72, 80, 192, 512, 80, 256, 88, 384, 192, 96, 96, 1024, 112, 80, 256, 384, 104, 144, 192, 1024, 320, 112, 120, 1024, 120, 128, 384, 512, 192, 384, 136, 512, 384, 256, 144, 1536 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Number of matrices M=[a,b;c,d] with 0<=a,b,c,d<n such that M*transpose(M)==[1,0;0,1] (mod n).

LINKS

Joerg Arndt, Table of n, a(n) for n = 1..1000

MATHEMATICA

gg[n_]:=gg[n]=Flatten[Table[{{x, y}, {z, t}}, {x, n}, {y, n}, {t, n}, {z, n}], 3]; orto[n_]:=orto[n]=Length@gg[n][[Select[Range[Length[gg[n]]], Mod[gg[n][[#]].Transpose[gg[n][[#]]], n]=={{1, 0}, {0, 1}}&]]]; Table[Print[orto[n]]; orto[n], {n, 1, 22}]

CROSSREFS

Cf.A209411

Sequence in context: A167592 A094513 A110004 * A174882 A080095 A193219

Adjacent sequences:  A182036 A182037 A182038 * A182040 A182041 A182042

KEYWORD

nonn,mult

AUTHOR

José María Grau Ribas, Apr 07 2012

EXTENSIONS

Terms beyond a(22) by Joerg Arndt, Apr 13 2012.

STATUS

approved

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Last modified November 18 17:56 EST 2017. Contains 294894 sequences.