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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. 1

%I

%S 25,81,257,833,2689,8705,28161,91137,294913,954369,3088385,9994241,

%T 32342017,104660993,338690049,1096024065,3546808321,11477712897,

%U 37142659073,120196169729,388962975745,1258710630401,4073273163777

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

%C Column 3 of A204713.

%H R. H. Hardin, <a href="/A204708/b204708.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +2*a(n-2) -4*a(n-3).

%F Conjectures from _Colin Barker_, Jun 09 2018: (Start)

%F G.f.: x*(25 + 6*x - 36*x^2) / ((1 - x)*(1 - 2*x - 4*x^2)).

%F a(n) = (5 + (20-8*sqrt(5))*(1-sqrt(5))^n + 4*(1+sqrt(5))^n*(5+2*sqrt(5))) / 5.

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A204713.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 18 2012

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Last modified October 16 12:23 EDT 2021. Contains 348041 sequences. (Running on oeis4.)