A181237 - OEIS

%I #21 Sep 08 2022 08:45:54

%S 14,182,3362,69302,1513514,34306274,798145922,18931023542,

%T 455746863002,11101993582682,273053990926082,6769463525042402,

%U 168956196145732802,4241145331821456002,106989959570749263362,2710690928812030164662

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

%C Row 3 of A181236.

%H Robert Israel, <a href="/A181237/b181237.txt">Table of n, a(n) for n = 1..630</a> (first 112 terms from R. H. Hardin)

%F From _Robert Israel_, Oct 30 2014: (Start)

%F a(n) = 2 * (1 + (3*n)!/(n!)^3).

%F a(n+1) = (3*(3*n+2)*(3*n+1)*a(n) - 52*n^2 - 50*n - 10)/(n+1)^2. (End)

%e All solutions for 3 X 3:

%e ..0..0..0....0..0..1....0..0..1....0..1..0....0..1..0....0..1..1....0..1..1

%e ..0..0..0....0..1..0....1..0..0....0..0..1....1..0..0....1..0..1....1..1..0

%e ..0..0..0....1..0..0....0..1..0....1..0..0....0..0..1....1..1..0....1..0..1

%e ...

%e ..1..0..0....1..0..0....1..0..1....1..0..1....1..1..0....1..1..0....1..1..1

%e ..0..0..1....0..1..0....0..1..1....1..1..0....0..1..1....1..0..1....1..1..1

%e ..0..1..0....0..0..1....1..1..0....0..1..1....1..0..1....0..1..1....1..1..1

%p seq(2 * (1 + (3*n)!/(n!)^3), n = 1 .. 20); # _Robert Israel_, Oct 30 2014

%t Table[2 (1 + (3 n)! / (n!)^3), {n, 20}] (* _Vincenzo Librandi_, Oct 30 2014 *)

%o (Magma) [2*(1+Factorial(3*n)/Factorial(n)^3): n in [1..20]]; // _Vincenzo Librandi_, Oct 30 2014

%Y Cf. A181236.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 10 2010