A346084 Number of invertible n X n cyclic matrices over GF(2).

1, 1, 5, 146, 17352, 8607552, 17362252800, 141087882903552, 4605333486987902976, 602440395156024780128256, 315546297657431573076891402240, 661423879140352987222707528171257856, 5547073628722488310034844542685201882415104, 186106159461598495645613441708238958650047305089024

Offset

0,3

Links

Table of n, a(n) for n=0..13.

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

Formula

Sum_{n>=0} a(n)x^n/A002884(n) = (1 + 2x/(2-x)* Product_{i>=2}(1 + x^i/((2^i-1)(1-x/2)^i)))^A001037(i).

Mathematica

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[Series[(1 + 2 x/(2 - x)) Product[(1 + 2^i x^i/((2^i - 1) (2^i - x^i)))^ A001037[[i]], {i, 2, nn}], {x, 0, nn}], x]

Crossrefs

Cf. A001037, A002884, A346082.

Sequence in context: A307902 A281427 A294360 * A075186 A352758 A226803

Adjacent sequences: A346081 A346082 A346083 * A346085 A346086 A346087

Keyword

nonn

Author

Geoffrey Critzer, Jul 04 2021

Status

approved