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A204708 Number of (n+1) X 4 0..1 arrays with the permanents of all 2 X 2 subblocks equal and nonzero.

%I A204708 #9 Jun 09 2018 06:49:36
%S A204708 25,81,257,833,2689,8705,28161,91137,294913,954369,3088385,9994241,
%T A204708 32342017,104660993,338690049,1096024065,3546808321,11477712897,
%U A204708 37142659073,120196169729,388962975745,1258710630401,4073273163777
%N A204708 Number of (n+1) X 4 0..1 arrays with the permanents of all 2 X 2 subblocks equal and nonzero.
%C A204708 Column 3 of A204713.
%H A204708 R. H. Hardin, <a href="/A204708/b204708.txt">Table of n, a(n) for n = 1..210</a>
%F A204708 Empirical: a(n) = 3*a(n-1) +2*a(n-2) -4*a(n-3).
%F A204708 Conjectures from _Colin Barker_, Jun 09 2018: (Start)
%F A204708 G.f.: x*(25 + 6*x - 36*x^2) / ((1 - x)*(1 - 2*x - 4*x^2)).
%F A204708 a(n) = (5 + (20-8*sqrt(5))*(1-sqrt(5))^n + 4*(1+sqrt(5))^n*(5+2*sqrt(5))) / 5.
%F A204708 (End)
%e A204708 Some solutions for n=4:
%e A204708 ..1..1..1..0....0..1..1..1....1..0..1..0....1..1..0..1....0..1..0..1
%e A204708 ..1..0..1..1....1..1..0..1....1..1..0..1....1..0..1..1....1..1..1..0
%e A204708 ..1..1..0..1....1..0..1..1....1..0..1..0....0..1..1..0....1..0..1..1
%e A204708 ..0..1..1..0....0..1..1..0....1..1..1..1....1..1..0..1....0..1..1..0
%e A204708 ..1..0..1..1....1..0..1..1....0..1..0..1....1..0..1..1....1..1..0..1
%Y A204708 Cf. A204713.
%K A204708 nonn
%O A204708 1,1
%A A204708 _R. H. Hardin_, Jan 18 2012