A054752 Number of inequivalent n X n matrices over GF(5) under action of dihedral group of the square D_4.

1, 5, 120, 252375, 19076074375, 37252918396015625, 1818989403666496277343750, 2220446049250331744551658935546875, 67762635780344027129112510010600128173828125, 51698788284564229679463057470911735435947895050048828125

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=5 of A343097.

Cf. A054247.

Formula

a(n) = 1/8*(5^(n^2) + 2*5^(n^2/4) + 3*5^(n^2/2) + 2*5^((n^2+n)/2)) if n is even;

a(n) = 1/8*(5^(n^2) + 2*5^((n^2+3)/4) + 5^((n^2+1)/2) + 4*5^((n^2+n)/2)) if n is odd.

Extensions

Terms a(9) and beyond from Andrew Howroyd, Apr 15 2021