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A224549 Number of (n+1) X 8 0..1 matrices with each 2 X 2 subblock idempotent.

%I A224549 #8 Aug 31 2018 06:37:56
%S A224549 216,345,472,682,943,1323,1858,2652,3845,5681,8544,13062,20247,31739,
%T A224549 50190,79892,127789,205117,330056,532022,858611,1386835,2241302,
%U A224549 3623632,5860053,9478413,15332788,24805102,40131355,64929471,105053374,169974912
%N A224549 Number of (n+1) X 8 0..1 matrices with each 2 X 2 subblock idempotent.
%C A224549 Column 7 of A224550.
%H A224549 R. H. Hardin, <a href="/A224549/b224549.txt">Table of n, a(n) for n = 1..210</a>
%F A224549 Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 2*a(n-4) - a(n-5) for n>6.
%F A224549 Empirical g.f.: x*(216 - 519*x + 172*x^2 + 303*x^3 - 202*x^4 + 15*x^5) / ((1 - x)^3*(1 - x - x^2)). - _Colin Barker_, Aug 31 2018
%e A224549 Some solutions for n=3:
%e A224549 ..1..1..1..0..0..1..0..0....1..0..0..0..0..0..0..0....1..1..1..0..0..0..0..0
%e A224549 ..0..0..0..0..0..1..0..1....1..0..0..0..0..0..0..0....0..0..0..0..0..0..0..0
%e A224549 ..0..0..0..0..0..1..0..1....1..0..0..0..0..0..0..0....0..0..0..0..0..0..0..0
%e A224549 ..0..0..0..0..0..1..0..1....0..0..0..0..0..1..1..1....0..0..0..0..0..0..1..1
%Y A224549 Cf. A224550.
%K A224549 nonn
%O A224549 1,1
%A A224549 _R. H. Hardin_, Apr 10 2013