%I #20 Nov 03 2023 15:13:11
%S 1,16,256,3844,58081,876096,13220496,199487376,3010168225,45421839376,
%T 685391917456,10342205764900,156058483721569,2354841001103616,
%U 35533320688065600,536179248686523456,8090664794986628449,122083905679560691216,1842182367418373568064
%N Number of 2 X n 0..3 arrays avoiding the pattern z-2 z-1 z in any row, column, nw-to-se diagonal or ne-to-sw antidiagonal.
%C Column and row 2 of A206838.
%H Alois P. Heinz, <a href="/A206840/b206840.txt">Table of n, a(n) for n = 0..1000</a> (terms n = 1..210 from R. H. Hardin)
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (16,-7,-120,282,-84,-42,0,7,-4,1).
%F a(n) = 16*a(n-1) -7*a(n-2) -120*a(n-3) +282*a(n-4) -84*a(n-5) -42*a(n-6) +7*a(n-8) -4*a(n-9) +a(n-10).
%F a(n) = A206839(n)^2. - _Mark van Hoeij_, May 14 2013
%F G.f.: (1 + 7*x^2 - 20*x^3 + 7*x^4 + x^6) / ((1 - 16*x + 14*x^2 - 4*x^3 + x^4)*(1 - 7*x^2 + 12*x^3 + 7*x^4 - x^6)). - _Colin Barker_, Jul 08 2019
%e Some solutions for n=5
%e ..1..3..3..1..3....3..3..1..0..0....3..3..3..3..1....2..0..2..0..3
%e ..2..2..1..1..3....2..1..2..1..0....1..1..3..1..1....3..1..0..1..0
%p a:= n-> ((<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <1|-2|0|4>>^n)[4$2])^2:
%p seq(a(n), n=0..25); # _Alois P. Heinz_, Oct 26 2016
%o (PARI) Vec((1 + 7*x^2 - 20*x^3 + 7*x^4 + x^6) / ((1 - 16*x + 14*x^2 - 4*x^3 + x^4)*(1 - 7*x^2 + 12*x^3 + 7*x^4 - x^6)) + O(x^20)) \\ _Colin Barker_, Jul 08 2019
%Y Cf. A206838, A206839.
%K nonn,easy
%O 0,2
%A _R. H. Hardin_, Feb 13 2012
%E a(0)=1 prepended by _Alois P. Heinz_, Oct 26 2016