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A053725 Number of n X n binary matrices of order dividing 3 (also number of solutions to X^3=I in GL(n,2)). 29
1, 3, 57, 1233, 75393, 19109889, 6326835201, 6388287561729, 23576681450405889, 120906321631678693377, 1968421511613895105052673, 111055505036706392268074909697, 8965464105556083354144035638870017 (list; graph; refs; listen; history; text; internal format)



V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.


Table of n, a(n) for n=1..13.

Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.


(PARI) \\ 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


Cf. A053722, A053846, A053856.

Cf. A053718, A053770, A053771, A053772, A053773, A053774, A053775, A053776, A053777.

Sequence in context: A139746 A273919 A157929 * A053774 A254570 A009723

Adjacent sequences:  A053722 A053723 A053724 * A053726 A053727 A053728




Vladeta Jovovic, Mar 23 2000



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Last modified January 18 04:47 EST 2019. Contains 319269 sequences. (Running on oeis4.)