A224686 - OEIS

%I #7 Sep 03 2018 03:49:56

%S 3465,1720,1896,2166,2429,2646,3214,4122,5307,6699,8253,10313,13224,

%T 17256,22621,29474,38326,50021,65685,86644,114391,150918,199073,

%U 262818,347453,459759,608521,805360,1065871,1410937,1868234,2474211,3276950

%N Number of (n+4) X 8 0..1 matrices with each 5 X 5 subblock idempotent.

%H R. H. Hardin, <a href="/A224686/b224686.txt">Table of n, a(n) for n = 1..210</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*(3465 - 8675*x + 3666*x^2 + 6848*x^3 - 7232*x^4 - 1677*x^5 + 5708*x^6 + 1572*x^7 - 5764*x^8 + 1869*x^9 + 158*x^10 + 56*x^11 + 4*x^12) / ((1 - x)^3*(1 + x)*(1 - x + x^2)*(1 - x^2 - x^3)). - _Colin Barker_, Sep 03 2018

%e Some solutions for n=2:

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

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

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

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

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

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

%Y Column 4 of A224690.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 15 2013