A204043
Circle Gaussian integer factorial, product of all Gaussian integers except 0 having an absolute value less than or equal to n.
Original entry on oeis.org
-1, 64, -207360000, 15161366937600000000, -16026514807440384000000000000000000000000, 9186394651457723405912022826165758590976000000000000000000000000
Offset: 1
a(1) = 1 * i * -1 * -i = -1. (Note that numbers like -1 + i are ignored here).
a(5) = 5 * (4 + 3i) * (3 + 4i) * 5i * (-3 + 4i) * (-4 + 3i) * ... (Note that the absolute value of numbers like 4 + 3i is precisely 5).
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Table[Times@@Select[ReplaceAll[Flatten[Table[a + b I, {a, -n, n}, {b, -n, n}]], 0 -> 1], Abs[#] <= n &], {n, 10}]
A204044
Lozenge Gaussian integer factorial, product of all nonzero Gaussian integers a + bi for which |a| + |b| <= n.
Original entry on oeis.org
-1, 64, -3240000, 530841600000000, -791432829997056000000000000, 24298387172648346846064803840000000000000000, -30208456145049398593072092383690495361024000000000000000000000000
Offset: 1
a(2) = -2 * (-1 - i) * -1 * (-1 + i) * -2i * -i * i * 2i * (1 - i) * 1 * (1 + i) * 2 = 64. (Note that numbers like -2 + i are skipped over in the computation of a(2) because abs(-2) + abs(1) > 2).
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Table[Times@@Select[ReplaceAll[Flatten[Table[a + b I, {a, -n, n}, {b, -n, n}]], 0 -> 1], Abs[Re[#]] + Abs[Im[#]] <= n&], {n, 10}]
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a(n)=(-1)^n*prod(i=1,n,prod(j=1,n-i,i^2+j^2))^2*n!^4 \\ Charles R Greathouse IV, May 01 2012
A236988
Real part of the product of all the Gaussian integers in the rectangle [1, 1] to [2, n].
Original entry on oeis.org
1, -20, 140, 200, -67600, 3983200, -228488000, 14375920000, -1002261520000, 74864404160000, -5398716356800000, 221997813232000000, 54286859023072000000, -27326116497867200000000, 9481971502321385600000000, -3155347494162485190400000000
Offset: 1
For n = 2, we have (1 + i)(1 + 2i)(2 + i)(2 + 2i) which gives -20 + 0i, so a(2) = -20.
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function cNumber(x, y) {
return [x, y];
}
function cMult(a, b) {
return [a[0] * b[0] - a[1] * b[1], a[0] * b[1] + a[1] * b[0]];
}
for (i = 1; i < 20; i++) {
c = cNumber(1, 0);
for (j = 1; j <= 2; j++)
for (k = 1; k <= i; k++)
c = cMult(c, cNumber(j, k));
document.write(c[0] + ", ");
}
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Table[Re[Times@@Flatten[Table[a + b I, {a, 2}, {b, n}]]], {n, 20}] (* Alonso del Arte, Feb 02 2014 *)
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a(n) = real(prod(i=1, 2, prod(j=1, n, i+I*j))); \\ Michel Marcus, Feb 03 2014
Showing 1-3 of 3 results.
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