A087918 - OEIS

A087918

Let A(n) be the matrix in the group GL(n,2) such that for 1<=i, j<=n: A[i,j] = 1 if i+j = n+1 A[i,j] = 0 if i+j != n+1. a(n) is the size of the conjugacy class of A(n) in GL(n,2).

1, 3, 21, 210, 6510, 234360, 29763720, 4047865920, 2068459485120, 1092146608143360, 2235624106869457920, 4650098142288472473600, 38088953883484878031257600, 314462403262051153026062745600, 10303989567687630131204997985075200, 338960040818652280796119613717033779200

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..16.

FORMULA

a(n) = A002884(n) / A087540(n).

PROG

(GAP)

a:=function(n) local M;

M:=NullMat(n, n); for i in [1..n] do M[i][n+1-i]:=1; od;

return Size(ConjugacyClass(GL(n, Integers mod 2), M * One(Integers mod 2)));

end; # Andrew Howroyd, Jul 13 2018

(PARI) \\ here b(n) is A002884.

b(n)={prod(i=2, n, 2^i-1)*2^binomial(n, 2)}

a(n)={my(m=n\2); b(n)/(2^(m*if(n%2, n+3, n)/2)*b(m))} \\ Andrew Howroyd, Jul 13 2018

CROSSREFS

Cf. A002884, A087540.

Sequence in context: A097690 A037967 A123691 * A088926 A291743 A339644

Adjacent sequences: A087915 A087916 A087917 * A087919 A087920 A087921

KEYWORD

nonn

AUTHOR

Yuval Dekel (dekelyuval(AT)hotmail.com), Oct 26 2003

EXTENSIONS

a(8)-a(16) from Andrew Howroyd, Jul 13 2018

STATUS

approved