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A183985 1/4 the number of (n+1) X 9 binary arrays with all 2 X 2 subblock sums the same.

%I A183985 #11 Aug 31 2024 15:42:36
%S A183985 153,155,158,164,174,194,230,302,438,710,1238,2294,4374,8534,16790,
%T A183985 33302,66198,131990,263318,525974,1050774,2100374,4198550,8394902,
%U A183985 16785558,33566870,67125398,134242454,268468374,536920214,1073807510,2147582102
%N A183985 1/4 the number of (n+1) X 9 binary arrays with all 2 X 2 subblock sums the same.
%C A183985 Column 8 of A183986.
%H A183985 R. H. Hardin, <a href="/A183985/b183985.txt">Table of n, a(n) for n = 1..200</a>
%H A183985 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3, 0, -6, 4).
%F A183985 Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).
%F A183985 Conjectures from _Colin Barker_, Apr 09 2018: (Start)
%F A183985 G.f.: x*(153 - 304*x - 307*x^2 + 608*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).
%F A183985 a(n) = 3*2^(n/2-1) + 2^(n-1) + 150 for n even.
%F A183985 a(n) = 2^(n-1) + 2^((n+1)/2) + 150 for n odd.
%F A183985 (End)
%F A183985 The above empirical formula is correct. See note from Andrew Howroyd in A183986.
%e A183985 Some solutions for 5 X 9:
%e A183985 ..0..0..1..1..1..0..0..1..1....0..1..0..0..1..1..1..1..1
%e A183985 ..1..1..0..0..0..1..1..0..0....1..0..1..1..0..0..0..0..0
%e A183985 ..0..0..1..1..1..0..0..1..1....0..1..0..0..1..1..1..1..1
%e A183985 ..1..1..0..0..0..1..1..0..0....1..0..1..1..0..0..0..0..0
%e A183985 ..0..0..1..1..1..0..0..1..1....0..1..0..0..1..1..1..1..1
%Y A183985 Cf. A183986.
%K A183985 nonn
%O A183985 1,1
%A A183985 _R. H. Hardin_, Jan 08 2011