|
%I #10 Sep 02 2018 17:10:41
%S 512,1280,3200,8000,22400,62720,175616,514304,1506176,4410944,
%T 13125248,39055616,116214272,347690240,1040220800,3112136000,
%U 9327881600,27958088960,83797669376,251316410624,753719509376,2260469570624
%N Number of (n+2) X 3 0..1 matrices with each 3 X 3 subblock having the same population.
%H R. H. Hardin, <a href="/A224644/b224644.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) - 3*a(n-2) + 12*a(n-3) - 48*a(n-4) + 36*a(n-5) - 27*a(n-6) + 108*a(n-7) - 81*a(n-8).
%F Empirical g.f.: 64*x*(8 - 12*x - 6*x^2 - 111*x^3 + 144*x^4 + 27*x^5 + 270*x^6 - 324*x^7) / ((1 - x)*(1 - 3*x)*(1 - 3*x^3)*(1 - 9*x^3)). - _Colin Barker_, Sep 02 2018
%e Some solutions for n=2:
%e ..1..1..0....1..1..1....1..1..0....1..0..0....0..1..0....0..1..0....0..1..1
%e ..1..0..0....1..1..0....0..1..0....0..1..1....1..1..1....0..0..1....0..1..1
%e ..1..1..1....0..0..1....0..0..1....0..1..0....0..0..0....1..1..1....1..1..1
%e ..1..0..1....1..1..1....1..1..0....0..0..1....1..0..0....0..0..1....1..1..0
%Y Column 1 of A224651.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 13 2013
| 