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%I #9 Jun 15 2018 11:01:25
%S 296,534,682,1581,2034,4711,6078,14101,18210,42271,54606,126799,
%T 163806,380385,491406,1141143,1474206,3423417,4422606,10270239,
%U 13267806,30810705,39803406,92432103,119410206,277296297,358230606,831888879
%N Number of (n+1) X 5 0..3 arrays with every 2 X 2 subblock having nonzero determinant and commuting with every horizontal or vertical neighbor.
%C Column 4 of A206343.
%H R. H. Hardin, <a href="/A206339/b206339.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) for n>13.
%F Empirical g.f.: x*(296 + 238*x - 740*x^2 + 185*x^3 + 9*x^4 - 20*x^5 + 8*x^6 - 8*x^7 + 8*x^8 - 8*x^9 + 8*x^10 + 10*x^11 + 2*x^12) / ((1 - x)*(1 - 3*x^2)). - _Colin Barker_, Jun 15 2018
%e Some solutions for n=4:
%e ..3..1..3..1..3....1..3..1..3..1....0..1..0..1..0....1..0..1..0..2
%e ..1..3..1..3..1....3..1..3..1..3....1..0..1..0..1....0..1..0..1..0
%e ..3..1..3..1..3....1..3..1..3..1....0..1..0..1..0....2..0..1..0..1
%e ..1..3..1..3..1....3..1..3..1..3....3..0..1..0..1....0..2..0..1..0
%e ..3..1..3..1..3....1..3..1..3..1....0..3..0..1..3....2..0..2..0..1
%Y Cf. A206343.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 06 2012
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