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%I #7 Feb 17 2018 05:32:23
%S 25,50,76,123,191,300,470,741,1173,1866,2980,4775,7671,12348,19906,
%T 32125,51885,83846,135548,219191,354515,573460,927706,1500873,2428261,
%U 3928790,6356680,10285071,16641323,26925936,43566770,70492185,114058401
%N Number of (n+1) X 3 0..2 matrices with each 2 X 2 subblock idempotent
%C Column 2 of A224676.
%H R. H. Hardin, <a href="/A224670/b224670.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 Conjectures from _Colin Barker_, Feb 17 2018: (Start)
%F G.f.: x*(25 - 50*x + x^2 + 44*x^3 - 21*x^4) / ((1 - x)^3*(1 - x - x^2)).
%F a(n) = -2 + 2^(1-n)*sqrt(5)*(-(1-sqrt(5))^(1+n) + (1+sqrt(5))^(1+n)) + 2*(1+n) + (1+n)*(2+n)/2.
%F (End)
%e Some solutions for n=3:
%e ..1..0..2....0..0..0....1..1..1....1..0..0....1..0..0....0..0..0....1..0..0
%e ..0..0..1....0..0..0....0..0..0....0..0..1....0..0..0....0..0..0....0..0..0
%e ..0..0..1....0..0..0....0..0..0....0..0..1....0..0..1....0..0..0....0..0..0
%e ..0..0..1....0..0..0....0..0..1....0..0..1....0..0..1....1..1..1....0..0..0
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 14 2013
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