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A183980 1/4 the number of (n+1) X 4 binary arrays with all 2 X 2 subblock sums the same.

%I A183980 #15 Aug 31 2024 15:39:26
%S A183980 9,11,14,20,30,50,86,158,294,566,1094,2150,4230,8390,16646,33158,
%T A183980 66054,131846,263174,525830,1050630,2100230,4198406,8394758,16785414,
%U A183980 33566726,67125254,134242310,268468230,536920070,1073807366,2147581958,4295098374
%N A183980 1/4 the number of (n+1) X 4 binary arrays with all 2 X 2 subblock sums the same.
%C A183980 Column 3 of A183986.
%H A183980 R. H. Hardin, <a href="/A183980/b183980.txt">Table of n, a(n) for n = 1..200</a>
%H A183980 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3, 0, -6, 4).
%F A183980 Empirical: a(n)=3*a(n-1)-6*a(n-3)+4*a(n-4).
%F A183980 Conjectures from _Colin Barker_, Apr 07 2018: (Start)
%F A183980 G.f.: x*(9 - 16*x - 19*x^2 + 32*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).
%F A183980 a(n) = (3*2^(n/2) + 2^n + 12) / 2 for n even.
%F A183980 a(n) = 2^((n-5)/2+3) + 2^(n-1) + 6 for n odd.
%F A183980 (End)
%F A183980 The above empirical formula is correct. See note from Andrew Howroyd in A183986.
%e A183980 Some solutions for 5 X 4.
%e A183980 ..0..1..0..1....1..1..1..1....0..0..1..1....1..0..1..0....1..1..1..0
%e A183980 ..1..1..1..1....0..0..0..0....1..1..0..0....1..1..1..1....0..0..0..1
%e A183980 ..1..0..1..0....1..1..1..1....0..0..1..1....1..0..1..0....1..1..1..0
%e A183980 ..1..1..1..1....0..0..0..0....1..1..0..0....1..1..1..1....0..0..0..1
%e A183980 ..0..1..0..1....1..1..1..1....0..0..1..1....0..1..0..1....1..1..1..0
%Y A183980 Cf. A183986.
%K A183980 nonn
%O A183980 1,1
%A A183980 _R. H. Hardin_, Jan 08 2011