A053725
Number of n X n binary matrices of order dividing 3 (also number of solutions to X^3=I in GL(n,2)).
Original entry on oeis.org
1, 3, 57, 1233, 75393, 19109889, 6326835201, 6388287561729, 23576681450405889, 120906321631678693377, 1968421511613895105052673, 111055505036706392268074909697, 8965464105556083354144035638870017
Offset: 1
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
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\\ See Morison theorem 2.6
\\ F(n,q,k) is number of solutions to X^k=I in GL(i, GF(q)) for i=1..n.
\\ q is power of prime and gcd(q, k) = 1.
B(n,q,e)={sum(m=0, n\e, x^(m*e)/prod(k=0, m-1, q^(m*e)-q^(k*e)))}
F(n,q,k)={if(gcd(q,k)<>1, error("no can do")); my(D=ffgen(q)^0); my(f=factor(D*(x^k-1))); my(p=prod(i=1, #f~, (B(n, q, poldegree(f[i,1])) + O(x*x^n))^f[i,2])); my(r=B(n,q,1)); vector(n, i, polcoeff(p, i)/polcoeff(r, i))}
F(10, 2, 3) \\ Andrew Howroyd, Jul 09 2018
A053857
Number of n X n matrices over GF(4) of order dividing 3 (i.e., number of solutions of X^3=I in GL(n,4)).
Original entry on oeis.org
3, 63, 8739, 5790339, 25502129667, 757411145447427, 118807204270671126531, 126820439575807166309695491, 924621244138490026408263487979523, 36417188783803065273959858411560634941443, 9819078516370596103771260673534011545166677016579
Offset: 1
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
A053860
Number of n X n matrices over GF(4) of order dividing 5 (i.e., number of solutions of X^5=I in GL(n,4)).
Original entry on oeis.org
1, 25, 8065, 15450625, 1157871796225, 87966277381914625, 163854915382616600346625, 2899292808403896778002083610625, 409353092294744973843137037325905690625, 1655314633158965843313074656520358690270555930625, 8042610863521667687144051842810375934526150927428955930625
Offset: 1
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
A053862
Number of n X n matrices over GF(4) of order dividing 7 (i.e., number of solutions of X^7=I in GL(n,4)).
Original entry on oeis.org
1, 1, 5761, 31334401, 136768389121, 820260207643852801, 18335066086016219275591681, 328113739821565326934355528908801, 13331506915406061943466437913131131863041, 709215733340453866919693651825288232662162472960001, 51979148071106263356020510647871238516054065671329809222860801
Offset: 1
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
Showing 1-4 of 4 results.