A224621 - OEIS

%I #9 Sep 02 2018 06:46:28

%S 32029,22081,26624,29254,30723,31623,39450,51956,66929,83137,100012,

%T 124474,161207,212671,280106,364172,472461,617237,813236,1076422,

%U 1423431,1878479,2478058,3273384,4331649,5736669,7596488,10055630,13309847

%N Number of (n+4) X 8 0..2 matrices with each 5 X 5 subblock idempotent.

%C Column 4 of A224625.

%H R. H. Hardin, <a href="/A224621/b224621.txt">Table of n, a(n) for n = 1..40</a>

%F Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - 2*a(n-6) + 2*a(n-8) - a(n-9) for n>13.

%F Empirical g.f.: x*(32029 - 74006*x + 24439*x^2 + 57602*x^3 - 55716*x^4 - 15033*x^5 + 48721*x^6 + 14698*x^7 - 49772*x^8 + 16668*x^9 + 300*x^10 + 64*x^11 + 4*x^12) / ((1 - x)^3*(1 + x)*(1 - x + x^2)*(1 - x^2 - x^3)). - _Colin Barker_, Sep 02 2018

%e Some solutions for n=2:

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

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

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

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

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

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

%Y Cf. A224625.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 12 2013