A224666 - OEIS

%I #10 Sep 02 2018 17:10:47

%S 78,108,142,180,222,268,318,372,430,492,558,628,702,780,862,948,1038,

%T 1132,1230,1332,1438,1548,1662,1780,1902,2028,2158,2292,2430,2572,

%U 2718,2868,3022,3180,3342,3508,3678,3852,4030,4212,4398,4588,4782,4980,5182

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

%H R. H. Hardin, <a href="/A224666/b224666.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*n^2 + 24*n + 52.

%F Conjectures from _Colin Barker_, Sep 02 2018: (Start)

%F G.f.: 2*x*(39 - 63*x + 26*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 ..1..0..0..0....1..0..0..0....1..1..0..1....1..0..1..0....1..0..0..0

%e ..0..0..0..0....1..0..0..1....0..0..0..1....0..0..1..0....1..0..0..0

%e ..0..0..0..0....1..0..0..1....0..0..0..1....0..0..1..0....1..0..0..0

%e ..0..0..0..1....0..0..0..1....0..0..0..1....0..0..1..0....0..0..1..1

%Y Row 4 of A224665.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 14 2013