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

1,1

Comments

Row 3 of A181236.

Links

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

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)

Example

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

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 *)

Prog

(Magma) [2*(1+Factorial(3*n)/Factorial(n)^3): n in [1..20]]; // Vincenzo Librandi, Oct 30 2014

Crossrefs

Cf. A181236.

Sequence in context: A170695 A170733 A186229 * A091030 A179090 A165152

Adjacent sequences: A181234 A181235 A181236 * A181238 A181239 A181240

Keyword

nonn

Author

R. H. Hardin, Oct 10 2010

Status

approved