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A181237
Number of (3n) X 3 binary matrices with all row sums equal and all column sums equal.
1
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Oct 10 2010
STATUS
approved