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Number of (n+2) X 8 0..1 matrices with each 3 X 3 subblock idempotent.
1

%I #8 Aug 31 2018 09:27:05

%S 418,351,451,551,740,992,1298,1742,2382,3267,4530,6362,9003,12826,

%T 18395,26514,38360,55674,81001,118063,172323,251789,368191,538722,

%U 788583,1154705,1691212,2477429,3629612,5318141,7792721,11419313,16734258

%N Number of (n+2) X 8 0..1 matrices with each 3 X 3 subblock idempotent.

%C Column 6 of A224559.

%H R. H. Hardin, <a href="/A224557/b224557.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(418 - 1321*x + 1555*x^2 - 1237*x^3 + 1159*x^4 - 767*x^5 + 184*x^6 + 4*x^7) / ((1 - x)^3*(1 - x - x^3)). - _Colin Barker_, Aug 31 2018

%e Some solutions for n=3:

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

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

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

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

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

%Y Cf. A224559.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 10 2013