A232820 - OEIS

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A232820

Imaginary part of the sum over the n-th powers of all Gaussian integers in the n X n base square in the first quadrant.

1, 18, 144, 0, -28200, -814968, -15203328, 0, 16696909080, 893794451000, 25789252433472, 0, -54804262577596532, -4044941639317807200, -161017938434267136000, 0, 621130358284578576358416, 59512584052525004199214632, 3008072527724272784969384000, 0

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Colin Barker, Table of n, a(n) for n = 1..200

FORMULA

Conjecture: a(4n) = 0. - Michel Marcus, Nov 09 2014

MATHEMATICA

g[n_] := Sum[(a + b I)^n, {a, 1, n}, {b, 1, n}]; Table[Im[g[n]], {n, 33}]

PROG

(PARI) vector(100, n, imag(sum(x=1, n, sum(y=1, n, (x+I*y)^n)))) \\ Colin Barker, Nov 09 2014

CROSSREFS