A074032 Number of degree-n irreducible polynomials over GF(4) with trace 0 and subtrace 1.

0, 0, 1, 4, 12, 40, 144, 512, 1813, 6528, 23808, 87380, 322560, 1198080, 4473647, 16777216, 63160320, 238605640, 904200192, 3435973836, 13089411609, 49977753600, 191219367936, 733007751680, 2814749599332, 10825959997440, 41699995927744, 160842843834660

Offset

1,4

Comments

Let a = RootOf( x^2+x+1 ) and b = 1+a. Same as number of degree-n irreducible polynomials over GF(4) with trace 0 and subtrace a. Same as number of degree-n irreducible polynomials over GF(4) with trace 0 and subtrace b.

Is this a duplicate of A074450? - R. J. Mathar, Dec 16 2020

Links

Table of n, a(n) for n=1..28.

E. N. Kuz'min, Irreducible polynomials over a finite field and an analogue of Gauss sums over a field of characteristic 2, Siberian Mathematical Journal, 32, 982-989 (1991).

Jon Maiga, Computer-generated formulas for A074032, Sequence Machine.

Frank Ruskey, Number of irreducible polynomials over GF(4) with given trace and subtrace

Formula

a(n) = A042979(2*n)/2 [discovered by Sequence Machine]. - Andrey Zabolotskiy, Oct 09 2021

Crossrefs

Cf. A074031, A074033, A074034, A074035, A042979.

Cf. A074450.

Sequence in context: A064649 A149332 A149333 * A074450 A028403 A149334

Adjacent sequences: A074029 A074030 A074031 * A074033 A074034 A074035

Keyword

nice,nonn

Author

Frank Ruskey and Nate Kube, Aug 26 2002

Extensions

More terms from Ruskey's website added by Joerg Arndt, Jan 16 2011

Terms a(17) and beyond from Andrey Zabolotskiy, Dec 15 2020

Status

approved