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 1-4 of 4 results.

A181237 Number of (3n) X 3 binary matrices with all row sums equal and all column sums equal.

Original entry on oeis.org

14, 182, 3362, 69302, 1513514, 34306274, 798145922, 18931023542, 455746863002, 11101993582682, 273053990926082, 6769463525042402, 168956196145732802, 4241145331821456002, 106989959570749263362, 2710690928812030164662
Offset: 1

Views

Author

R. H. Hardin, Oct 10 2010

Keywords

Comments

Row 3 of A181236.

Examples

			All solutions for 3 X 3:
..0..0..0....0..0..1....0..0..1....0..1..0....0..1..0....0..1..1....0..1..1
..0..0..0....0..1..0....1..0..0....0..0..1....1..0..0....1..0..1....1..1..0
..0..0..0....1..0..0....0..1..0....1..0..0....0..0..1....1..1..0....1..0..1
...
..1..0..0....1..0..0....1..0..1....1..0..1....1..1..0....1..1..0....1..1..1
..0..0..1....0..1..0....0..1..1....1..1..0....0..1..1....1..0..1....1..1..1
..0..1..0....0..0..1....1..1..0....0..1..1....1..0..1....0..1..1....1..1..1

Links

Crossrefs

Cf. A181236.

Programs

  • Magma
    [2*(1+Factorial(3*n)/Factorial(n)^3): n in [1..20]]; // Vincenzo Librandi, Oct 30 2014
  • Maple
    seq(2 * (1 + (3*n)!/(n!)^3), n = 1 .. 20); # Robert Israel, Oct 30 2014
  • Mathematica
    Table[2 (1 + (3 n)! / (n!)^3), {n, 20}] (* Vincenzo Librandi, Oct 30 2014 *)

Formula

From Robert Israel, Oct 30 2014: (Start)
a(n) = 2 * (1 + (3*n)!/(n!)^3).
a(n+1) = (3*(3*n+2)*(3*n+1)*a(n) - 52*n^2 - 50*n - 10)/(n+1)^2. (End)

A181238 Number of (4*n)X4 binary matrices with all row sums equal and all column sums equal.

Original entry on oeis.org

140, 49772, 33235358, 27896484332, 26012734507190, 25785064658274014, 26631749414632177802, 28342597507242978860012, 30862541359435652055581702, 34221243248277031078812700022, 38507504930060734566868274154362
Offset: 1

Views

Author

R. H. Hardin Oct 10 2010

Keywords

Comments

Row 4 of A181236

Examples

			Some solutions for 4X4
..1..1..0..1....1..1..0..0....0..1..0..1....0..1..0..0....1..0..0..1
..1..0..1..1....0..0..1..1....1..0..0..1....0..0..0..1....1..1..0..0
..0..1..1..1....1..0..0..1....0..1..1..0....0..0..1..0....0..0..1..1
..1..1..1..0....0..1..1..0....1..0..1..0....1..0..0..0....0..1..1..0

Links

A181234 Number of (2*n)Xn binary matrices with all row sums equal and all column sums equal.

Original entry on oeis.org

2, 8, 182, 49772, 113400002, 4027811102702, 1237505791330809002
Offset: 1

Views

Author

R. H. Hardin Oct 10 2010

Keywords

Comments

Column 2 of A181236

Examples

			Some solutions for 6X3
..1..0..0....0..1..1....1..0..0....1..1..0....0..1..0....1..0..0....0..0..1
..0..1..0....1..0..1....0..1..0....1..1..0....1..0..0....0..0..1....1..0..0
..1..0..0....1..1..0....0..0..1....0..1..1....0..0..1....0..1..0....0..1..0
..0..0..1....1..1..0....0..0..1....0..1..1....0..1..0....0..1..0....1..0..0
..0..0..1....0..1..1....1..0..0....1..0..1....0..0..1....0..0..1....0..1..0
..0..1..0....1..0..1....0..1..0....1..0..1....1..0..0....1..0..0....0..0..1

A181235 Number of (3*n)Xn binary matrices with all row sums equal and all column sums equal.

Original entry on oeis.org

2, 22, 3362, 33235358, 5210265060002, 90698868503010138802
Offset: 1

Views

Author

R. H. Hardin Oct 10 2010

Keywords

Comments

Column 3 of A181236

Examples

			Some solutions for 9X3
..0..1..1....0..1..1....1..1..0....0..0..1....1..0..0....1..0..1....0..1..0
..0..1..1....1..0..1....1..0..1....0..1..0....0..1..0....1..0..1....1..0..0
..1..1..0....1..0..1....0..1..1....1..0..0....0..0..1....1..1..0....0..1..0
..1..1..0....1..1..0....0..1..1....1..0..0....1..0..0....1..0..1....0..1..0
..0..1..1....0..1..1....1..1..0....0..1..0....1..0..0....0..1..1....0..0..1
..1..0..1....0..1..1....1..0..1....1..0..0....0..0..1....0..1..1....1..0..0
..1..0..1....1..1..0....1..0..1....0..0..1....0..0..1....0..1..1....0..0..1
..1..1..0....1..1..0....0..1..1....0..0..1....0..1..0....1..1..0....0..0..1
..1..0..1....1..0..1....1..1..0....0..1..0....0..1..0....1..1..0....1..0..0
Showing 1-4 of 4 results.

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