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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

%I

%S 1,3,21,210,6510,234360,29763720,4047865920,2068459485120,

%T 1092146608143360,2235624106869457920,4650098142288472473600,

%U 38088953883484878031257600,314462403262051153026062745600,10303989567687630131204997985075200,338960040818652280796119613717033779200

%N 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).

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

%o (GAP)

%o a:=function(n) local M;

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

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

%o end; # _Andrew Howroyd_, Jul 13 2018

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

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

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

%Y Cf. A002884, A087540.

%K nonn

%O 1,2

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

%E a(8)-a(16) from _Andrew Howroyd_, Jul 13 2018

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Last modified October 4 06:38 EDT 2022. Contains 357237 sequences. (Running on oeis4.)