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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. 1

%I

%S 45,47,50,56,66,86,122,194,330,602,1130,2186,4266,8426,16682,33194,

%T 66090,131882,263210,525866,1050666,2100266,4198442,8394794,16785450,

%U 33566762,67125290,134242346,268468266,536920106,1073807402,2147581994,4295098410

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

%C Column 6 of A183986.

%H R. H. Hardin, <a href="/A183983/b183983.txt">Table of n, a(n) for n = 1..200</a>

%F Conjectures from _Colin Barker_, Apr 09 2018: (Start)

%F G.f.: x*(45 - 88*x - 91*x^2 + 176*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

%F a(n) = 3*2^(n/2-1) + 2^(n-1) + 42 for n even.

%F a(n) = 2^(n-1) + 2^((n+1)/2) + 42 for n odd.

%F a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4) for n>4.

%F (End)

%e Some solutions for 5 X 7.

%e ..0..0..1..0..1..0..1....1..0..1..0..1..0..1....0..1..0..1..0..1..0

%e ..1..1..0..1..0..1..0....0..0..0..0..0..0..0....0..1..0..1..0..1..0

%e ..0..0..1..0..1..0..1....1..0..1..0..1..0..1....0..1..0..1..0..1..0

%e ..1..1..0..1..0..1..0....0..0..0..0..0..0..0....0..1..0..1..0..1..0

%e ..0..0..1..0..1..0..1....1..0..1..0..1..0..1....0..1..0..1..0..1..0

%Y Cf. A183986.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 08 2011

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Last modified March 22 11:07 EDT 2023. Contains 361423 sequences. (Running on oeis4.)