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A204748 Number of (n+2) X 4 0..1 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly three ways, and new values 0..1 introduced in row major order. 1

%I

%S 61,46,31,28,38,49,70,106,159,248,394,625,1002,1614,2599,4196,6782,

%T 10961,17726,28674,46383,75040,121410,196433,317826,514246,832055,

%U 1346284,2178326,3524593,5702902,9227482,14930367,24157832,39088186,63246001

%N Number of (n+2) X 4 0..1 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly three ways, and new values 0..1 introduced in row major order.

%C Column 2 of A204754.

%H R. H. Hardin, <a href="/A204748/b204748.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) +a(n-2) +a(n-3) -a(n-4) -a(n-5) for n>8.

%F Empirical g.f.: x*(61 - 15*x - 76*x^2 - 110*x^3 - 6*x^4 + 59*x^5 + 32*x^6 + 8*x^7) / ((1 - x)*(1 - x - x^2)*(1 + x + x^2)). - _Colin Barker_, Jun 09 2018

%e Some solutions for n=3:

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

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

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

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

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

%Y Cf. A204754.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 18 2012

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Last modified January 22 19:45 EST 2022. Contains 350504 sequences. (Running on oeis4.)