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

1,1

Comments

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

Links

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

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}]

Prog

(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

Crossrefs

Cf. A230308, A230310.

Sequence in context: A270400 A269999 A298944 * A102275 A299448 A300086

Adjacent sequences: A230306 A230307 A230308 * A230310 A230311 A230312

Keyword

nonn

Author

José María Grau Ribas, Oct 16 2013

Status

approved