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A177793 Partial sums of A054247. 1

%I

%S 1,3,9,111,8659,4220403,8594777715,70377477369459,2305913405481561715,

%T 302233760834929839713907,158456627262298939528655810163,

%U 332307157402856267706609817833582195

%N Partial sums of A054247.

%C 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?

%F 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].

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

%o Contribution from _R. J. Mathar_, May 28 2010: (Start)

%o (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) ; }

%o A177793(n)={ return(sum(i=0,n,A054247(i))) ; }

%o { for(n=0,20, print1(A177793(n),",") ; ) ; } (End)

%Y Cf. A002724, A054247, A054407.

%K easy,nonn

%O 0,2

%A _Jonathan Vos Post_, May 13 2010

%E Extended by _R. J. Mathar_, May 28 2010

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Last modified June 19 09:44 EDT 2021. Contains 345126 sequences. (Running on oeis4.)