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A184040 1/9 the number of (n+1) X (n+1) 0..2 arrays with all 2 X 2 subblocks having the same four values.

%I A184040 #9 Mar 09 2024 16:25:54
%S A184040 9,21,41,81,153,297,569,1113,2169,4281,8441,16761,33273,66297,132089,
%T A184040 263673,526329,1051641,2101241,4200441,8396793,16789497,33570809,
%U A184040 67133433,134250489,268484601,536936441,1073840121,2147614713,4295163897,8590196729,17180262393
%N A184040 1/9 the number of (n+1) X (n+1) 0..2 arrays with all 2 X 2 subblocks having the same four values.
%H A184040 Andrew Howroyd, <a href="/A184040/b184040.txt">Table of n, a(n) for n = 1..1000</a>
%H A184040 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-6,4).
%F A184040 From _Andrew Howroyd_, Mar 09 2024: (Start)
%F A184040 a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).
%F A184040 G.f.: x*(9 - 6*x - 22*x^2 + 12*x^3)/((1 - x)*(1 - 2*x)*(1 - 2*x^2)). (End)
%e A184040 Some solutions for 5X5
%e A184040 ..1..0..1..0..1....1..2..1..0..1....1..0..1..0..1....0..1..0..1..0
%e A184040 ..1..0..1..0..1....0..0..0..2..0....2..0..2..0..2....1..1..1..1..1
%e A184040 ..0..1..0..1..0....1..2..1..0..1....0..1..0..1..0....1..0..1..0..1
%e A184040 ..0..1..0..1..0....0..0..0..2..0....0..2..0..2..0....1..1..1..1..1
%e A184040 ..0..1..0..1..0....1..2..1..0..1....1..0..1..0..1....0..1..0..1..0
%o A184040 (PARI) Vec((9 - 6*x - 22*x^2 + 12*x^3)/((1 - x)*(1 - 2*x)*(1 - 2*x^2)) + O(x^32)) \\ _Andrew Howroyd_, Mar 09 2024
%Y A184040 Diagonal of A184048.
%K A184040 nonn,easy
%O A184040 1,1
%A A184040 _R. H. Hardin_, Jan 08 2011
%E A184040 a(15) onwards from _Andrew Howroyd_, Mar 09 2024