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A184065 Number of (n+1) X 4 binary arrays with rows and columns in nondecreasing order and with no 2 X 2 subblock sum differing from a horizontal or vertical neighbor subblock sum by more than one. 1

%I

%S 20,36,130,382,924,1884,3463,5800,9065,13397,18940,25837,34232,44269,

%T 56092,69845,85672,103717,124124,147037,172600,200957,232252,266629,

%U 304232,345205,389692,437837,489784,545677,605660,669877,738472,811589

%N Number of (n+1) X 4 binary arrays with rows and columns in nondecreasing order and with no 2 X 2 subblock sum differing from a horizontal or vertical neighbor subblock sum by more than one.

%C Column 3 of A184071.

%H R. H. Hardin, <a href="/A184065/b184065.txt">Table of n, a(n) for n = 1..200</a>

%F Conjectures from _Colin Barker_, Apr 11 2018: (Start)

%F G.f.: x*(20 - 44*x + 106*x^2 - 2*x^3 + 52*x^4 - 4*x^5 + 73*x^6 - 62*x^7 + 31*x^8 - 31*x^9 + 5*x^10 - x^11 + x^12) / (1 - x)^4.

%F a(n) = 757 + 14*n - 115*n^2 + 24*n^3 for n>9.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>13.

%F (End)

%e Some solutions for 3 X 4:

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

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

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

%e ...

%e ...2..3..4.......2..2..2.......1..2..2.......1..2..2.......1..2..3...

%e ...3..3..4.......2..1..2.......2..3..3.......2..3..2.......2..1..2...

%Y Cf. A184071.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 09 2011

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Last modified January 27 01:03 EST 2021. Contains 340443 sequences. (Running on oeis4.)