cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A204041 Square Gaussian integer factorial, product of all Gaussian integers except 0 having a real or imaginary part less than or equal to n.

Original entry on oeis.org

-4, 2560000, -19188605030400000000, 26257841860510325145600000000000000000000, -50074374492086859469933185828103742596055040000000000000000000000000000
Offset: 1

Views

Author

Alonso del Arte, Jan 09 2012

Keywords

Comments

This is called "square" because the Gaussian integers involved here form a square on the complex plane.
All terms are purely real integers, but a(6) has more than a hundred digits.

Examples

			a(1) = 1 * (1 + i) * i * (-1 + i) * -1 * (-1 - i) * -i * (1 - i) = -4.
		

Crossrefs

Cf. A204044, lozenge factorial; A204043, circle factorial.

Programs

  • Mathematica
    Table[Times@@ReplaceAll[Flatten[Table[a + b I, {a, -n, n}, {b, -n, n}]], 0 -> 1], {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

Views

Author

Alonso del Arte, Jan 09 2012

Keywords

Comments

Called "lozenge" because the Gaussian integers considered here form up a lozenge or diamond in the complex plane.
All terms are purely real integers.

Examples

			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).
		

Crossrefs

Cf. A204041, square factorial; A204043, circle factorial.

Programs

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

Formula

log |a(n)| ~ 2n^2 log n. - Charles R Greathouse IV, May 01 2012
Showing 1-2 of 2 results.