cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A346082 Number of cyclic n X n matrices over GF(2).

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%I A346082 #14 Aug 24 2021 06:49:42
%S A346082 1,2,14,412,50832,25517184,51759986688,422000664182784,
%T A346082 13794938575436906496,1805965390215106718072832,
%U A346082 946278871976706458877777936384,1983897413727786229545246093886881792,16639646499680599124923569106989157705580544,558292116984541859085729903695019486031085083557888
%N A346082 Number of cyclic n X n matrices over GF(2).
%C A346082 An n X n matrix A is cyclic if there is a vector v in GF(2)^n such that {A^i(v) : i>=0} spans GF(2)^n. Equivalently if the characteristic polynomial of A is equal to the minimal polynomial.
%H A346082 Kent E. Morrison, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Morrison/morrison37.html">Integer Sequences and Matrices Over Finite Fields</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
%F A346082 Sum_{n>=0} a(n) x^n/A002884(n) = Product_{i>=1} (1 + x^i/((2^i-1)(1-x/2)^i))^A001037(i).
%t A346082 nn = 13; A001037 = Table[1/n Sum[MoebiusMu[n/d] 2^d, {d, Divisors[n]}], {n, 1, nn}]; Table[Product[2^n - 2^i, {i, 0, n - 1}], {n, 0, nn}] CoefficientList[
%t A346082   Series[Product[(1 + 2^i x^i/((2^i - 1) (2^i - x^i)))^ A001037[[i]], {i, 1, nn}], {x, 0, nn}], x]
%Y A346082 Cf. A001037, A002884.
%Y A346082 Main diagonal of A347010.
%K A346082 nonn
%O A346082 0,2
%A A346082 _Geoffrey Critzer_, Jul 04 2021