A224727 - OEIS

%I #8 Sep 04 2018 14:36:02

%S 8117,5711,6540,7132,7575,9090,11268,13821,16593,20653,26657,34977,

%T 45825,60486,80897,109371,148429,201881,275470,377256,517816,711541,

%U 978561,1347070,1855835,2558018,3526907,4863988,6709510,9256888,12772821

%N Number of (n+3) X 10 0..2 matrices with each 4 X 4 subblock idempotent.

%H R. H. Hardin, <a href="/A224727/b224727.txt">Table of n, a(n) for n = 1..100</a>

%F Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 4*a(n-4) - 3*a(n-5) + 2*a(n-7) - a(n-8) for n>10.

%F Empirical g.f.: x*(8117 - 18640*x + 5641*x^2 + 15168*x^3 - 21787*x^4 + 15216*x^5 + 4385*x^6 - 11795*x^7 + 3637*x^8 + 48*x^9) / ((1 - x)^3*(1 + x)*(1 - x - x^4)). - _Colin Barker_, Sep 04 2018

%e Some solutions for n=2:

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

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

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

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

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

%Y Column 7 of A224728.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 16 2013