A184540 - OEIS

%I #9 Apr 12 2018 22:24:34

%S 45,89,147,220,309,415,539,682,845,1029,1235,1464,1717,1995,2299,2630,

%T 2989,3377,3795,4244,4725,5239,5787,6370,6989,7645,8339,9072,9845,

%U 10659,11515,12414,13357,14345,15379,16460,17589,18767,19995,21274,22605,23989

%N Number of (n+2) X 3 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

%C Column 1 of A184548.

%H R. H. Hardin, <a href="/A184540/b184540.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = (84 + 149*n + 36*n^2 + n^3) / 6. Corrected by _Colin Barker_, Apr 12 2018~

%F Conjectures from _Colin Barker_, Apr 12 2018: (Start)

%F G.f.: x*(45 - 91*x + 61*x^2 - 14*x^3) / (1 - x)^4.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

%F (End)

%e Some solutions for 4 X 3:

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

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

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

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

%Y Cf. A184548.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 16 2011