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%I #8 Sep 01 2018 09:17:30
%S 452,370,512,739,990,1345,1852,2659,3846,5589,8064,11675,16954,24757,
%T 36196,52963,77458,113341,165916,243035,356062,521713,764408,1120079,
%U 1641326,2405317,3525004,5165987,7570886,11095421,16260864,23831255
%N Number of (n+3) X 4 0..1 matrices with each 4 X 4 subblock idempotent.
%C Column 1 of A224568.
%H R. H. Hardin, <a href="/A224561/b224561.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-4) - 2*a(n-5) + 2*a(n-6) - 2*a(n-7) + a(n-8) for n>10.
%F Empirical g.f.: x*(452 - 986*x + 758*x^2 - 139*x^3 - 513*x^4 + 614*x^5 - 628*x^6 + 597*x^7 - 168*x^8 - 13*x^9) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 - x - x^3)). - _Colin Barker_, Sep 01 2018
%e Some solutions for n=3:
%e ..1..0..0..0....1..0..1..0....1..0..0..0....0..0..0..0....1..1..0..1
%e ..0..1..0..1....0..1..1..1....0..0..0..0....0..1..1..1....0..0..0..0
%e ..0..0..0..0....0..0..0..0....0..0..1..1....0..0..0..0....0..0..0..0
%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e ..0..1..0..1....0..1..1..1....0..0..1..1....0..1..1..1....1..1..1..1
%e ..0..1..0..1....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%Y Cf. A224568.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 10 2013
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