A177793 Partial sums of A054247.

1, 3, 9, 111, 8659, 4220403, 8594777715, 70377477369459, 2305913405481561715, 302233760834929839713907, 158456627262298939528655810163, 332307157402856267706609817833582195

Offset: 0

Author

Jonathan Vos Post, May 13 2010

Keywords

• easy
• nonn

Comments

Partial sums of number of n X n binary matrices under action of dihedral group of the square D_4. Can this ever be prime?

Examples

			a(4) = 1 + 2 + 6 + 102 + 8548 = 8659 = 7 * 1237.
		

Crossrefs

Cf. A002724, A054247, A054407.

Programs

PARI

A054247(n)={ local(a) ; if(n%2==0, a=2^(n^2)+2*2^(n^2/4)+3*2^(n^2/2)+2*2^((n^2+n)/2), a=2^(n^2)+2*2^((n^2+3)/4)+2^((n^2+1)/2)+4*2^((n^2+n)/2); ) ; return(a/8) ; }
A177793(n)={ return(sum(i=0,n,A054247(i))) ; }
{ for(n=0,20, print1(A177793(n),",") ; ) ; } (End)

Formula

a(n) = SUM[i=0..n] A054247(i) = SUM[i=0..n] [(1/8)*(2^(i^2)+2*2^(i^2/4)+3*2^(i^2/2)+2*2^((i^2+i)/2)) if i is even and (1/8)*(2^(i^2)+2*2^((i^2+3)/4)+2^((i^2+1)/2)+4*2^((i^2+i)/2)) if i is odd].

Extensions

Extended by R. J. Mathar, May 28 2010