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A224545 Number of (n+1) X 4 0..1 matrices with each 2 X 2 subblock idempotent.

%I A224545 #7 Aug 30 2018 15:49:30
%S A224545 28,52,78,125,193,302,472,743,1175,1868,2982,4777,7673,12350,19908,
%T A224545 32127,51887,83848,135550,219193,354517,573462,927708,1500875,2428263,
%U A224545 3928792,6356682,10285073,16641325,26925938,43566772,70492187,114058403
%N A224545 Number of (n+1) X 4 0..1 matrices with each 2 X 2 subblock idempotent.
%C A224545 Column 3 of A224550.
%H A224545 R. H. Hardin, <a href="/A224545/b224545.txt">Table of n, a(n) for n = 1..210</a>
%F A224545 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 A224545 Empirical g.f.: x*(28 - 60*x + 10*x^2 + 45*x^3 - 25*x^4 + x^5) / ((1 - x)^3*(1 - x - x^2)). - _Colin Barker_, Aug 30 2018
%e A224545 Some solutions for n=3:
%e A224545 ..1..0..0..0....1..1..0..0....1..1..0..1....1..0..0..0....1..0..1..0
%e A224545 ..1..0..0..0....0..0..0..0....0..0..0..1....1..0..0..0....1..0..1..0
%e A224545 ..0..0..0..0....0..0..0..0....0..0..0..1....0..0..0..0....1..0..1..0
%e A224545 ..0..0..0..1....1..1..1..1....0..0..0..1....0..0..1..1....1..0..1..0
%Y A224545 Cf. A224550.
%K A224545 nonn
%O A224545 1,1
%A A224545 _R. H. Hardin_, Apr 10 2013