A224555 - OEIS

%I #8 Aug 31 2018 09:27:16

%S 172,174,230,286,395,551,749,1041,1473,2086,2973,4273,6166,8925,12962,

%T 18869,27511,40165,58700,85850,125626,183908,269310,394457,577854,

%U 846620,1240499,1817740,2663711,3903524,5720540,8383488,12286209,18005905

%N Number of (n+2) X 6 0..1 matrices with each 3 X 3 subblock idempotent.

%C Column 4 of A224559.

%H R. H. Hardin, <a href="/A224555/b224555.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 6*a(n-2) + 5*a(n-3) - 4*a(n-4) + 3*a(n-5) - a(n-6) for n>8.

%F Empirical g.f.: x*(172 - 514*x + 566*x^2 - 450*x^3 + 449*x^4 - 283*x^5 + 55*x^6 + 4*x^7) / ((1 - x)^3*(1 - x - x^3)). - _Colin Barker_, Aug 31 2018

%e Some solutions for n=3:

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

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

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

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

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

%Y Cf. A224559.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 10 2013