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

%I A181237 #21 Sep 08 2022 08:45:54
%S A181237 14,182,3362,69302,1513514,34306274,798145922,18931023542,
%T A181237 455746863002,11101993582682,273053990926082,6769463525042402,
%U A181237 168956196145732802,4241145331821456002,106989959570749263362,2710690928812030164662
%N A181237 Number of (3n) X 3 binary matrices with all row sums equal and all column sums equal.
%C A181237 Row 3 of A181236.
%H A181237 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 A181237 From _Robert Israel_, Oct 30 2014: (Start)
%F A181237 a(n) = 2 * (1 + (3*n)!/(n!)^3).
%F A181237 a(n+1) = (3*(3*n+2)*(3*n+1)*a(n) - 52*n^2 - 50*n - 10)/(n+1)^2. (End)
%e A181237 All solutions for 3 X 3:
%e A181237 ..0..0..0....0..0..1....0..0..1....0..1..0....0..1..0....0..1..1....0..1..1
%e A181237 ..0..0..0....0..1..0....1..0..0....0..0..1....1..0..0....1..0..1....1..1..0
%e A181237 ..0..0..0....1..0..0....0..1..0....1..0..0....0..0..1....1..1..0....1..0..1
%e A181237 ...
%e A181237 ..1..0..0....1..0..0....1..0..1....1..0..1....1..1..0....1..1..0....1..1..1
%e A181237 ..0..0..1....0..1..0....0..1..1....1..1..0....0..1..1....1..0..1....1..1..1
%e A181237 ..0..1..0....0..0..1....1..1..0....0..1..1....1..0..1....0..1..1....1..1..1
%p A181237 seq(2 * (1 + (3*n)!/(n!)^3), n = 1 .. 20); # _Robert Israel_, Oct 30 2014
%t A181237 Table[2 (1 + (3 n)! / (n!)^3), {n, 20}] (* _Vincenzo Librandi_, Oct 30 2014 *)
%o A181237 (Magma) [2*(1+Factorial(3*n)/Factorial(n)^3): n in [1..20]]; // _Vincenzo Librandi_, Oct 30 2014
%Y A181237 Cf. A181236.
%K A181237 nonn
%O A181237 1,1
%A A181237 _R. H. Hardin_, Oct 10 2010