A054407 Number of asymmetric n X n binary matrices under action of dihedral group of the square D_4.

0, 0, 0, 36, 7860, 4177152, 8589313152, 70368605798400, 2305842990423490560, 302231454885790246502400, 158456325028519245775644917760, 332306998946228931044233275859009536, 2787593149816327892614636032925171439370240

Offset: 0

Author

Vladeta Jovovic, May 08 2000

Keywords

• easy
• nonn

Links

• Colin Barker, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A054247.

Formula

(1/8)*(2^(n^2)-2*2^((n^2+n)/2)-3*2^(n^2/2)+2*2^(n^2/4)+2*2^((n^2+2*n)/4)) if n is even and (1/8)*(2^(n^2)-4*2^((n^2+n)/2)-2^((n^2+1)/2)+4*2^((n^2+2*n+1)/4)) if n is odd. - Corrected by Colin Barker, Oct 25 2016

Extensions

More terms from Colin Barker, Oct 25 2016