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A089036 Number of n X n matrices over GF(3) with characteristic polynomial x^n - 1. 3

%I

%S 1,12,729,758160,2972290464,354396766517640,92079975413927255040,

%T 939180873931369976460153600,22528399544939174411840147874772641,

%U 11276516942788127325350557035641264267894784,25780902234356363794160964471948503247074139517747200

%N Number of n X n matrices over GF(3) with characteristic polynomial x^n - 1.

%H I. Reiner, <a href="https://projecteuclid.org/euclid.ijm/1255629830">On the number of matrices with given characteristic polynomial</a>, Illinois J. Math. 5 1961 324-329.

%o (PARI) \\ see Reiner reference.

%o F(u,r)={prod(i=1, r, (1-u^(-i)))}

%o a(n, q=3)={my(D=ffgen(q)); my(f=factor(D^0*(x^n-1))); q^(n^2-n)*F(q,n)/prod(i=1, #f~, F(q^poldegree(f[i,1]), f[i,2]))} \\ _Andrew Howroyd_, Jul 08 2018

%Y Cf. A088654, A089035, A089037.

%K nonn

%O 1,2

%A Yuval Dekel (dekelyuval(AT)hotmail.com) and _W. Edwin Clark_, Nov 29 2003

%E Offset corrected and a(9)-a(11) from _Andrew Howroyd_, Jul 08 2018

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Last modified August 7 15:36 EDT 2022. Contains 355989 sequences. (Running on oeis4.)