A224622 - OEIS

%I #8 Sep 02 2018 06:46:24

%S 39001,23453,28058,30723,32204,33115,41120,53862,69089,85561,102702,

%T 127605,165006,217389,285998,371501,481659,628969,828412,1096213,

%U 1449265,1912222,2522235,3331436,4408182,5837723,7729963,10231957,13542892

%N Number of (n+4) X 9 0..2 matrices with each 5 X 5 subblock idempotent.

%C Column 5 of A224625.

%H R. H. Hardin, <a href="/A224622/b224622.txt">Table of n, a(n) for n = 1..53</a>

%F Empirical: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4) +a(n-5) -3*a(n-6) +3*a(n-7) -a(n-8) for n>12.

%F Empirical g.f.: x*(39001 - 132551*x + 168252*x^2 - 96795*x^3 + 22849*x^4 - 39143*x^5 + 100600*x^6 - 84723*x^7 + 22198*x^8 + 256*x^9 + 50*x^10 + 5*x^11) / ((1 - x)^3*(1 - x + x^2)*(1 - x^2 - x^3)). - _Colin Barker_, Sep 02 2018

%e Some solutions for n=2:

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

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

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

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

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

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

%Y Cf. A224625.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 12 2013