%I #8 Aug 30 2018 16:00:24
%S 48,86,125,196,294,448,682,1049,1626,2543,4007,6355,10131,16216,26035,
%T 41894,67524,108962,175976,284371,459720,743401,1202365,1944941,
%U 3146409,5090378,8235737,13324984,21559506,34883188,56441302,91323005,147762726
%N Number of (n+1) X 5 0..1 matrices with each 2 X 2 subblock idempotent.
%C Column 4 of A224550.
%H R. H. Hardin, <a href="/A224546/b224546.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 2*a(n-4) - a(n-5) for n>6.
%F Empirical g.f.: x*(48 - 106*x + 21*x^2 + 78*x^3 - 47*x^4 + 3*x^5) / ((1 - x)^3*(1 - x - x^2)). - _Colin Barker_, Aug 30 2018
%e Some solutions for n=3:
%e ..1..0..1..0..0....0..1..0..0..1....1..0..1..0..0....1..0..0..0..0
%e ..1..0..1..0..1....0..1..0..0..1....0..0..1..0..0....1..0..0..0..0
%e ..1..0..1..0..1....0..1..0..0..1....0..0..1..0..0....1..0..0..0..1
%e ..0..0..1..0..1....0..1..0..0..1....0..0..1..0..1....1..0..0..0..1
%Y Cf. A224550.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 10 2013