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%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
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