|
%I #10 Jun 14 2018 12:00:16
%S 49,361,1600,9409,47089,258064,1343281,7198489,37945600,201895681,
%T 1068570721,5672499856,30061664689,159465247561,845443470400,
%U 4483691905729,23774527583569,126075439502224,668536407557041
%N Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having zero permanent.
%C Column 1 of A206255.
%H R. H. Hardin, <a href="/A206248/b206248.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) +12*a(n-2) -27*a(n-3).
%F a(n) = A006139(n+2)^2.
%F Conjectures from _Colin Barker_, Jun 14 2018: (Start)
%F G.f.: x*(49 + 165*x - 432*x^2) / ((1 + 3*x)*(1 - 7*x + 9*x^2)).
%F a(n) = 2^(-n)*((-1)^n*2^(1+n)*3^(3+n) + (77-20*sqrt(13))*(7-sqrt(13))^n + (7+sqrt(13))^n*(77+20*sqrt(13))) / 13.
%F (End)
%e Some solutions for n=4:
%e ..1..0....2..1....2..1....2..3....2..3....3..3....3..3....0..3....0..3....0..1
%e ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..2....0..2....0..0
%e ..0..3....1..0....2..1....2..3....0..0....1..1....3..1....0..3....0..0....0..1
%e ..0..1....2..0....0..0....0..0....0..0....0..0....0..0....0..2....3..3....0..2
%e ..0..3....1..0....3..0....1..3....3..0....1..1....0..1....0..1....0..0....0..2
%Y Cf. A206255.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 05 2012
| 