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A183977 1/4 the number of (n+1) X (n+1) binary arrays with all 2 X 2 subblock sums the same.

%I A183977 #19 Oct 16 2024 09:21:18
%S A183977 4,8,14,26,46,86,158,302,574,1118,2174,4286,8446,16766,33278,66302,
%T A183977 132094,263678,526334,1051646,2101246,4200446,8396798,16789502,
%U A183977 33570814,67133438,134250494,268484606,536936446,1073840126,2147614718,4295163902
%N A183977 1/4 the number of (n+1) X (n+1) binary arrays with all 2 X 2 subblock sums the same.
%H A183977 Andrew Howroyd, <a href="/A183977/b183977.txt">Table of n, a(n) for n = 1..1000</a>
%H A183977 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-6,4).
%F A183977 From _Andrew Howroyd_, Mar 09 2024: (Start)
%F A183977 a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).
%F A183977 G.f.: 2*x*(2 - 2*x - 5*x^2 + 4*x^3)/((1 - x)*(1 - 2*x)*(1 - 2*x^2)). (End)
%F A183977 E.g.f.: 3*cosh(sqrt(2)*x) + cosh(2*x) - 2*cosh(x) - 2  - 2*sinh(x) + sinh(2*x) + 2*sqrt(2)*sinh(sqrt(2)*x). - _Stefano Spezia_, Oct 16 2024
%e A183977 Some solutions for 5X5
%e A183977 ..1..0..1..0..1....0..1..0..1..0....1..1..1..1..1....0..1..1..0..1
%e A183977 ..1..0..1..0..1....1..0..1..0..1....0..1..0..1..0....1..0..0..1..0
%e A183977 ..0..1..0..1..0....1..0..1..0..1....1..1..1..1..1....0..1..1..0..1
%e A183977 ..1..0..1..0..1....1..0..1..0..1....1..0..1..0..1....1..0..0..1..0
%e A183977 ..0..1..0..1..0....1..0..1..0..1....1..1..1..1..1....0..1..1..0..1
%o A183977 (PARI) Vec(2*(2 - 2*x - 5*x^2 + 4*x^3)/((1 - x)*(1 - 2*x)*(1 - 2*x^2)) + O(x^32)) \\ _Andrew Howroyd_, Mar 09 2024
%Y A183977 Diagonal of A183986.
%K A183977 nonn,easy
%O A183977 1,1
%A A183977 _R. H. Hardin_, Jan 08 2011
%E A183977 a(19) onwards from _Andrew Howroyd_, Mar 09 2024