A224659 - OEIS

%I #8 Feb 17 2018 05:32:09

%S 3,12,50,108,260,542,1126,2230,4336,8246,15458,28608,52420,95240,

%T 171814,308056,549384,975130,1723482,3034498,5324180,9311762,16238070

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

%C Column 2 of A224665.

%F Empirical: a(n) = 6*a(n-1) -12*a(n-2) +5*a(n-3) +12*a(n-4) -12*a(n-5) -3*a(n-6) +6*a(n-7) -a(n-9) for n>10.

%F Empirical g.f.: x*(3 - 6*x + 14*x^2 - 63*x^3 + 116*x^4 - 80*x^5 + 7*x^6 + 12*x^8 + 3*x^9) / ((1 - x)^3*(1 - x - x^2)^3). - _Colin Barker_, Feb 17 2018

%e Some solutions for n=3:

%e ..1..0..0....1..0..0....1..1..2....1..0..1....1..0..2....1..0..0....1..1..1

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

%e ..2..1..1....2..0..1....0..1..1....0..0..1....0..0..1....0..1..1....1..1..1

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 14 2013