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

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

Offset: 1

Author

R. H. Hardin, Oct 10 2010

Keywords

• nonn

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

• Robert Israel, Table of n, a(n) for n = 1..630 (first 112 terms from R. H. Hardin)

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)