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A184030 1/16 the number of (n+1) X (n+1) 0..3 arrays with all 2 X 2 subblocks having the same four values.

%I A184030 #9 Mar 09 2024 16:25:59
%S A184030 16,40,82,166,322,634,1234,2434,4786,9490,18802,37426,74482,148594,
%T A184030 296434,592114,1182706,2363890,4724722,9446386,18886642,37767154,
%U A184030 75522034,151031794,302039026,604053490,1208057842,2416066546,4832034802,9663971314,19327746034,38655295474
%N A184030 1/16 the number of (n+1) X (n+1) 0..3 arrays with all 2 X 2 subblocks having the same four values.
%H A184030 Andrew Howroyd, <a href="/A184030/b184030.txt">Table of n, a(n) for n = 1..1000</a>
%H A184030 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-6,4).
%F A184030 From _Andrew Howroyd_, Mar 09 2024: (Start)
%F A184030 a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).
%F A184030 G.f.: 2*x*(8 - 4*x - 19*x^2 + 8*x^3)/((1 - x)*(1 - 2*x)*(1 - 2*x^2)). (End)
%e A184030 Some solutions for 4X4
%e A184030 ..1..3..1..1....3..0..3..0....2..2..2..2....0..0..0..0....1..0..0..0
%e A184030 ..1..1..1..3....0..1..0..1....1..3..1..3....2..2..2..2....0..2..1..2
%e A184030 ..1..3..1..1....0..3..0..3....2..2..2..2....0..0..0..0....1..0..0..0
%e A184030 ..1..1..1..3....1..0..1..0....3..1..3..1....2..2..2..2....0..2..1..2
%o A184030 (PARI) Vec(2*(8 - 4*x - 19*x^2 + 8*x^3)/((1 - x)*(1 - 2*x)*(1 - 2*x^2)) + O(x^30)) \\ _Andrew Howroyd_, Mar 09 2024
%Y A184030 Diagonal of A184039.
%K A184030 nonn,easy
%O A184030 1,1
%A A184030 _R. H. Hardin_, Jan 08 2011
%E A184030 a(14) onwards from _Andrew Howroyd_, Mar 09 2024