A230309 Sum_{0<=a<24*n, 0<=b<24*n} (a+b*i)^(24*n) (mod 24*n), where i is the imaginary unit.

8, 32, 0, 32, 80, 0, 56, 128, 0, 80, 176, 0, 104, 272, 0, 128, 272, 0, 152, 320, 0, 176, 368, 0, 200, 416, 0, 416, 464, 0, 248, 512, 0, 272, 560, 0, 296, 608, 0, 320, 656, 432, 344, 704, 0, 368, 752, 0, 392, 800, 0, 416, 848, 0, 560, 320, 0, 464, 944, 0, 488

Offset: 1

Author

José María Grau Ribas, Oct 16 2013

Keywords

• nonn

Comments

If m <> 0 (mod 24) then Sum_{(a+b*i)^m: 0<=a

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A230308, A230310.

Programs

Mathematica

aa[n_] := aa[n] = Mod[Sum[PowerMod[a + b *I, n, n], {a, n}, {b, n}], n]; Table[aa[24*n],{n,1,10}]

PARI

a(n)=my(N=24*n,a);lift(sum(A=0,N-1,a=Mod(A,N);sum(b=0,N-1,(a+b*I)^N))) \\ Charles R Greathouse IV, Nov 05 2013

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