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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)
 OFFSET 1,2 REFERENCES V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished. LINKS Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1. PROG (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 CROSSREFS 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 KEYWORD nonn AUTHOR Vladeta Jovovic, Mar 23 2000 STATUS approved

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