

A204043


Circle Gaussian integer factorial, product of all Gaussian integers except 0 having an absolute value less than or equal to n.


2




OFFSET

1,2


COMMENTS

Called "circle" because drawing a circle on the complex plane centered at 0 with radius n encloses the integers (with the exception of 0) that will be considered in computing a(n).
All terms of this sequence are purely real numbers.


LINKS

Table of n, a(n) for n=1..6.


EXAMPLE

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).


MATHEMATICA

Table[Times@@Select[ReplaceAll[Flatten[Table[a + b I, {a, n, n}, {b, n, n}]], 0 > 1], Abs[#] <= n &], {n, 10}]


CROSSREFS

Cf. A204041, square factorial; A204044, lozenge factorial.
Sequence in context: A017418 A017550 A087928 * A295175 A279290 A034061
Adjacent sequences: A204040 A204041 A204042 * A204044 A204045 A204046


KEYWORD

sign


AUTHOR

Alonso del Arte, Jan 09 2012


STATUS

approved



