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A183983 1/4 the number of (n+1) X 7 binary arrays with all 2 X 2 subblock sums the same.

%I A183983 #10 Aug 31 2024 15:41:22
%S A183983 45,47,50,56,66,86,122,194,330,602,1130,2186,4266,8426,16682,33194,
%T A183983 66090,131882,263210,525866,1050666,2100266,4198442,8394794,16785450,
%U A183983 33566762,67125290,134242346,268468266,536920106,1073807402,2147581994,4295098410
%N A183983 1/4 the number of (n+1) X 7 binary arrays with all 2 X 2 subblock sums the same.
%C A183983 Column 6 of A183986.
%H A183983 R. H. Hardin, <a href="/A183983/b183983.txt">Table of n, a(n) for n = 1..200</a>
%H A183983 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3, 0, -6, 4).
%F A183983 Conjectures from _Colin Barker_, Apr 09 2018: (Start)
%F A183983 G.f.: x*(45 - 88*x - 91*x^2 + 176*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).
%F A183983 a(n) = 3*2^(n/2-1) + 2^(n-1) + 42 for n even.
%F A183983 a(n) = 2^(n-1) + 2^((n+1)/2) + 42 for n odd.
%F A183983 a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4) for n>4.
%F A183983 (End)
%F A183983 The above empirical formula is correct. See note from Andrew Howroyd in A183986.
%e A183983 Some solutions for 5 X 7.
%e A183983 ..0..0..1..0..1..0..1....1..0..1..0..1..0..1....0..1..0..1..0..1..0
%e A183983 ..1..1..0..1..0..1..0....0..0..0..0..0..0..0....0..1..0..1..0..1..0
%e A183983 ..0..0..1..0..1..0..1....1..0..1..0..1..0..1....0..1..0..1..0..1..0
%e A183983 ..1..1..0..1..0..1..0....0..0..0..0..0..0..0....0..1..0..1..0..1..0
%e A183983 ..0..0..1..0..1..0..1....1..0..1..0..1..0..1....0..1..0..1..0..1..0
%Y A183983 Cf. A183986.
%K A183983 nonn
%O A183983 1,1
%A A183983 _R. H. Hardin_, Jan 08 2011