A224688 - OEIS

%I #7 Sep 03 2018 11:37:23

%S 5385,2110,2354,2646,2926,3158,3819,4858,6192,7747,9470,11789,15081,

%T 19640,25686,33386,43335,56505,74162,97792,129048,170178,224402,

%U 296206,391562,518095,685678,907404,1200852,1589573,2104743,2787411,3691719

%N Number of (n+4) X 10 0..1 matrices with each 5 X 5 subblock idempotent.

%H R. H. Hardin, <a href="/A224688/b224688.txt">Table of n, a(n) for n = 1..210</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*(5385 - 19430*x + 26224*x^2 - 15650*x^3 + 3411*x^4 - 5361*x^5 + 14558*x^6 - 12707*x^7 + 3439*x^8 + 69*x^9 + 57*x^10 + 4*x^11) / ((1 - x)^3*(1 - x + x^2)*(1 - x^2 - x^3)). - _Colin Barker_, Sep 03 2018

%e Some solutions for n=2:

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

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

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

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

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

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

%Y Column 6 of A224690.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 15 2013