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%I #10 Sep 02 2018 12:09:31
%S 196,260,332,412,500,596,700,812,932,1060,1196,1340,1492,1652,1820,
%T 1996,2180,2372,2572,2780,2996,3220,3452,3692,3940,4196,4460,4732,
%U 5012,5300,5596,5900,6212,6532,6860,7196,7540,7892,8252,8620,8996,9380,9772,10172
%N Number of 5 X 5 0..n matrices with each 2 X 2 subblock idempotent.
%H R. H. Hardin, <a href="/A224667/b224667.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*n^2 + 52*n + 140.
%F Conjectures from _Colin Barker_, Sep 02 2018: (Start)
%F G.f.: 4*x*(49 - 82*x + 35*x^2) / (1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
%F (End)
%e Some solutions for n=3:
%e ..0..1..0..0..1....1..0..1..0..0....1..0..1..0..0....1..0..1..0..0
%e ..0..1..0..0..1....1..0..1..0..1....1..0..1..0..1....1..0..1..0..0
%e ..0..1..0..0..1....0..0..1..0..1....1..0..1..0..1....1..0..1..0..0
%e ..0..1..0..0..1....0..0..1..0..1....1..0..1..0..1....1..0..1..0..1
%e ..0..1..0..0..1....0..0..1..0..1....0..0..1..0..1....2..0..1..0..1
%Y Row 5 of A224665.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 14 2013
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