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A224666 Number of 4 X 4 0..n matrices with each 2 X 2 subblock idempotent.

%I A224666 #10 Sep 02 2018 17:10:47
%S A224666 78,108,142,180,222,268,318,372,430,492,558,628,702,780,862,948,1038,
%T A224666 1132,1230,1332,1438,1548,1662,1780,1902,2028,2158,2292,2430,2572,
%U A224666 2718,2868,3022,3180,3342,3508,3678,3852,4030,4212,4398,4588,4782,4980,5182
%N A224666 Number of 4 X 4 0..n matrices with each 2 X 2 subblock idempotent.
%H A224666 R. H. Hardin, <a href="/A224666/b224666.txt">Table of n, a(n) for n = 1..210</a>
%F A224666 Empirical: a(n) = 2*n^2 + 24*n + 52.
%F A224666 Conjectures from _Colin Barker_, Sep 02 2018: (Start)
%F A224666 G.f.: 2*x*(39 - 63*x + 26*x^2) / (1 - x)^3.
%F A224666 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
%F A224666 (End)
%e A224666 Some solutions for n=3:
%e A224666 ..1..0..0..0....1..0..0..0....1..1..0..1....1..0..1..0....1..0..0..0
%e A224666 ..0..0..0..0....1..0..0..1....0..0..0..1....0..0..1..0....1..0..0..0
%e A224666 ..0..0..0..0....1..0..0..1....0..0..0..1....0..0..1..0....1..0..0..0
%e A224666 ..0..0..0..1....0..0..0..1....0..0..0..1....0..0..1..0....0..0..1..1
%Y A224666 Row 4 of A224665.
%K A224666 nonn
%O A224666 1,1
%A A224666 _R. H. Hardin_, Apr 14 2013