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Number of (2+1) X (n+1) 0..1 arrays with no 2 X 2 subblock having x11-x00 less than x10-x01.
1

%I #7 Nov 27 2018 11:37:11

%S 35,114,313,772,1775,3894,8277,17224,35339,71834,145137,292108,586471,

%T 1175678,2354637,4713168,9430915,18867170,37740521,75488148,150984415,

%U 301978054,603966533,1207944792,2415902715,4831820074,9663656417

%N Number of (2+1) X (n+1) 0..1 arrays with no 2 X 2 subblock having x11-x00 less than x10-x01.

%H R. H. Hardin, <a href="/A251269/b251269.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 14*a(n-2) + 16*a(n-3) - 9*a(n-4) + 2*a(n-5).

%F Conjectures from _Colin Barker_, Nov 27 2018: (Start)

%F G.f.: x*(35 - 96*x + 119*x^2 - 70*x^3 + 16*x^4) / ((1 - x)^4*(1 - 2*x)).

%F a(n) = 8*(9*2^n-8) - (109*n)/3 - 8*n^2 - (2*n^3)/3.

%F (End)

%e Some solutions for n=4:

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

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

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

%Y Row 2 of A251268.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 01 2014