The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A042979 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A042979

Number of degree-n irreducible polynomials over GF(2) with trace = 0 and subtrace = 1.
(history; published version)

#38 by Alois P. Heinz at Tue Apr 30 12:05:44 EDT 2019

STATUS

proposed

approved

#37 by Michel Marcus at Tue Apr 30 10:44:54 EDT 2019

STATUS

editing

proposed

#36 by Michel Marcus at Tue Apr 30 10:44:50 EDT 2019

CROSSREFS

Cf. A042979-A042980, A042981, A042982.

Cf. A074027-, A074028, A074029, A074030.

STATUS

proposed

editing

#35 by Torsten Muetze at Tue Apr 30 10:42:45 EDT 2019

STATUS

editing

proposed

#34 by Torsten Muetze at Tue Apr 30 10:42:38 EDT 2019

LINKS

F. Ruskey, <a href="http://www.theory.cs.uviccombos.ca/~cos/inf/neckorg/TraceSubtracePoly.htmlTSpoly">Number of irreducible polynomials over GF(2) with given trace and subtrace</a>

STATUS

approved

editing

Discussion

Tue Apr 30

10:42

Torsten Muetze: Repaired broken link

#33 by Alois P. Heinz at Sun Aug 19 19:41:51 EDT 2018

STATUS

proposed

approved

#32 by Andrew Howroyd at Sun Aug 19 12:16:51 EDT 2018

STATUS

editing

proposed

Discussion

Sun Aug 19

17:39

Jon E. Schoenfield: Thanks!

#31 by Andrew Howroyd at Sun Aug 19 12:14:35 EDT 2018

FORMULA

a(n) = (1/n) * Sum_{k=0..n, n+k == 0 (mod 4)} L(n, k), where L(n, k) = Sum_{d|gcd(n, k)} mu(d)*binomial(n/d, k/d).

STATUS

reviewed

editing

Discussion

Sun Aug 19

12:16

Andrew Howroyd: The formula needed an additional constraint on k. (there are a infinite number of k with n + k == 0 (mod 4)). [see PARI/mathematica progs]

#30 by Joerg Arndt at Sun Aug 19 11:25:06 EDT 2018

STATUS

proposed

reviewed

#29 by Jon E. Schoenfield at Sun Aug 19 10:20:07 EDT 2018

STATUS

editing

proposed