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A183984 1/4 the number of (n+1) X 8 binary arrays with all 2 X 2 subblock sums the same.

%I A183984 #10 Aug 31 2024 15:41:56
%S A183984 81,83,86,92,102,122,158,230,366,638,1166,2222,4302,8462,16718,33230,
%T A183984 66126,131918,263246,525902,1050702,2100302,4198478,8394830,16785486,
%U A183984 33566798,67125326,134242382,268468302,536920142,1073807438,2147582030
%N A183984 1/4 the number of (n+1) X 8 binary arrays with all 2 X 2 subblock sums the same.
%C A183984 Column 7 of A183986.
%H A183984 R. H. Hardin, <a href="/A183984/b183984.txt">Table of n, a(n) for n = 1..200</a>
%H A183984 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3, 0, -6, 4).
%F A183984 Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).
%F A183984 Conjectures from _Colin Barker_, Apr 09 2018: (Start)
%F A183984 G.f.: x*(81 - 160*x - 163*x^2 + 320*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).
%F A183984 a(n) = 3*2^(n/2-1) + 2^(n-1) + 78 for n even.
%F A183984 a(n) = 2^(n-1) + 2^((n+1)/2) + 78 for n odd.
%F A183984 (End)
%F A183984 The above empirical formula is correct. See note from Andrew Howroyd in A183986.
%e A183984 Some solutions for 5 X 8.
%e A183984 ..0..0..1..1..1..1..0..1....1..1..0..1..1..0..1..1....1..0..1..0..1..0..1..0
%e A183984 ..1..1..0..0..0..0..1..0....0..0..1..0..0..1..0..0....1..1..1..1..1..1..1..1
%e A183984 ..0..0..1..1..1..1..0..1....1..1..0..1..1..0..1..1....0..1..0..1..0..1..0..1
%e A183984 ..1..1..0..0..0..0..1..0....0..0..1..0..0..1..0..0....1..1..1..1..1..1..1..1
%e A183984 ..0..0..1..1..1..1..0..1....1..1..0..1..1..0..1..1....1..0..1..0..1..0..1..0
%Y A183984 Cf. A183986.
%K A183984 nonn
%O A183984 1,1
%A A183984 _R. H. Hardin_, Jan 08 2011