A054751 Number of inequivalent n X n matrices over GF(4) under action of dihedral group of the square D_4.

1, 4, 55, 34960, 537157696, 140738033618944, 590295811483987148800, 39614081257168338331296071680, 42535295865117309120430975675097153536, 730750818665451459102461990840694008379514814464, 200867255532373784442745261867639247948787687313041365401600

Offset: 0

Author

Vladeta Jovovic, May 15 2000

Keywords

• easy
• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..25

Crossrefs

Column k=4 of A343097.

Cf. A054247.

Programs

Mathematica

Table[If[EvenQ[n],(4^n^2+2*4^(n^2/4)+3*4^(n^2/2)+2*4^((n^2+n)/2))/8,(4^n^2+2*4^((n^2+3)/4)+4^((n^2+1)/2)+4*4^((n^2+n)/2))/8],{n,0,10}] (* Harvey P. Dale, Aug 16 2021 *)

Formula

a(n) = 1/8*(4^(n^2) + 2*4^(n^2/4) + 3*4^(n^2/2) + 2*4^((n^2+n)/2)) if n is even;

a(n) = 1/8*(4^(n^2) + 2*4^((n^2+3)/4) + 4^((n^2+1)/2) + 4*4^((n^2+n)/2)) if n is odd.

Extensions

Terms a(10) and beyond from Andrew Howroyd, Apr 15 2021