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A183979 1/4 the number of (n+1) X 3 binary arrays with all 2 X 2 subblock sums the same.

%I A183979 #17 Aug 31 2024 15:38:43
%S A183979 6,8,11,17,27,47,83,155,291,563,1091,2147,4227,8387,16643,33155,66051,
%T A183979 131843,263171,525827,1050627,2100227,4198403,8394755,16785411,
%U A183979 33566723,67125251,134242307,268468227,536920067,1073807363,2147581955,4295098371
%N A183979 1/4 the number of (n+1) X 3 binary arrays with all 2 X 2 subblock sums the same.
%C A183979 Column 2 of A183986.
%H A183979 R. H. Hardin, <a href="/A183979/b183979.txt">Table of n, a(n) for n = 1..200</a>
%H A183979 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3, 0, -6, 4).
%F A183979 Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).
%F A183979 Conjectures from _Colin Barker_, Apr 07 2018: (Start)
%F A183979 G.f.: x*(6 - 10*x - 13*x^2 + 20*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).
%F A183979 a(n) = (3*2^(n/2) + 2^n + 6) / 2 for n even.
%F A183979 a(n) = 2^(n-1) + 2^((n+1)/2) + 3 for n odd.
%F A183979 (End)
%F A183979 The above empirical formula is correct. See note from Andrew Howroyd in A183986.
%e A183979 Some solutions for 5 X 3.
%e A183979 ..1..0..1....1..0..1....1..0..1....1..0..1....0..1..0....1..0..1....1..0..1
%e A183979 ..0..1..0....1..1..1....0..1..0....0..0..0....0..1..0....1..0..1....1..0..1
%e A183979 ..0..1..0....0..1..0....0..1..0....1..0..1....1..0..1....0..1..0....0..1..0
%e A183979 ..0..1..0....1..1..1....1..0..1....0..0..0....1..0..1....0..1..0....1..0..1
%e A183979 ..0..1..0....0..1..0....0..1..0....1..0..1....1..0..1....0..1..0....0..1..0
%Y A183979 Cf. A183986.
%K A183979 nonn
%O A183979 1,1
%A A183979 _R. H. Hardin_, Jan 08 2011