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%I #8 Aug 30 2018 16:06:51
%S 8,32,78,196,428,916,1858,3678,7096,13458,25150,46466,85028,154356,
%T 278298,498792,889320,1578248,2789166,4910498,8615348,15067462,
%U 26274538,45693286
%N Number of (n+1) X (n+1) 0..1 matrices with each 2 X 2 subblock idempotent.
%C Diagonal of A224550.
%F Empirical: a(n) = 6*a(n-1) - 12*a(n-2) + 5*a(n-3) + 12*a(n-4) - 12*a(n-5) - 3*a(n-6) + 6*a(n-7) - a(n-9).
%F Empirical g.f.: 2*x*(4 - 8*x - 9*x^2 + 36*x^3 - 34*x^4 + 11*x^5 - 5*x^6 + 7*x^7 + x^8) / ((1 - x)^3*(1 - x - x^2)^3). - _Colin Barker_, Aug 30 2018
%e Some solutions for n=3:
%e ..0..1..0..0....0..0..0..0....1..1..0..0....0..0..0..0....0..0..0..0
%e ..0..1..0..0....0..0..0..0....0..0..0..0....0..0..0..0....1..1..1..1
%e ..0..1..0..1....0..0..0..0....0..0..0..1....1..1..1..1....0..0..0..0
%e ..0..1..0..1....0..1..1..1....0..0..0..1....0..0..0..0....0..1..1..1
%Y Cf. A224550.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 10 2013