%I #7 Aug 30 2018 15:49:21

%S 16,32,52,86,137,218,345,547,869,1385,2214,3549,5702,9178,14794,23872,

%T 38551,62292,100695,162821,263331,425947,689052,1114751,1803532,

%U 2917988,4721200,7638842,12359669,19998110,32357349,52354999,84711857,137066333

%N Number of (n+1) X 3 0..1 matrices with each 2 X 2 subblock idempotent.

%C Column 2 of A224550.

%H R. H. Hardin, <a href="/A224544/b224544.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).

%F Empirical g.f.: x*(16 - 32*x + 4*x^2 + 22*x^3 - 11*x^4) / ((1 - x)^3*(1 - x - x^2)). - _Colin Barker_, Aug 30 2018

%e Some solutions for n=3:

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

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

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

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

%Y Cf. A224550.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 10 2013