cp's OEIS Frontend

A204707 Number of (n+1) X 3 0..1 arrays with the permanents of all 2 X 2 subblocks equal and nonzero.

%I A204707 #9 Jun 09 2018 06:49:39
%S A204707 13,33,81,209,529,1361,3473,8913,22801,58449,149649,383441,982033,
%T A204707 2515793,6443921,16507089,42282769,108311121,277442193,710686673,
%U A204707 1820455441,4663202129,11945023889,30597832401,78377927953,200769257553
%N A204707 Number of (n+1) X 3 0..1 arrays with the permanents of all 2 X 2 subblocks equal and nonzero.
%C A204707 Column 2 of A204713.
%H A204707 R. H. Hardin, <a href="/A204707/b204707.txt">Table of n, a(n) for n = 1..210</a>
%F A204707 Empirical: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3).
%F A204707 Conjectures from _Colin Barker_, Jun 09 2018: (Start)
%F A204707 G.f.: x*(13 + 7*x - 24*x^2) / ((1 - x)*(1 - x - 4*x^2)).
%F A204707 a(n) = 1 + (2^(-1-n)*((1-sqrt(17))^n*(-19+5*sqrt(17)) + (1+sqrt(17))^n*(19+5*sqrt(17)))) / sqrt(17).
%F A204707 (End)
%e A204707 Some solutions for n=4:
%e A204707 ..1..0..1....0..1..0....1..1..1....0..1..1....1..1..0....0..1..1....0..1..1
%e A204707 ..1..1..1....1..1..1....0..1..0....1..0..1....0..1..1....1..1..0....1..0..1
%e A204707 ..1..0..1....1..0..1....1..1..1....1..1..0....1..0..1....0..1..1....1..1..1
%e A204707 ..1..1..1....0..1..0....1..0..1....0..1..1....1..1..0....1..1..0....1..0..1
%e A204707 ..1..0..1....1..1..1....0..1..1....1..1..0....0..1..1....1..0..1....0..1..1
%Y A204707 Cf. A204713.
%K A204707 nonn
%O A204707 1,1
%A A204707 _R. H. Hardin_, Jan 18 2012