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A204376 Number of (n+2) X 5 0..1 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically or nw-to-se diagonally exactly three ways, and new values 0..1 introduced in row major order. 1

%I

%S 78,54,61,75,98,139,205,310,481,759,1206,1931,3105,5002,8073,13043,

%T 21082,34091,55141,89198,144305,233471,377742,611179,988889,1600034,

%U 2588889,4188891,6777746,10966603,17744317,28710886,46455169,75166023,121621158

%N Number of (n+2) X 5 0..1 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically or nw-to-se diagonally exactly three ways, and new values 0..1 introduced in row major order.

%C Column 3 of A204381.

%H R. H. Hardin, <a href="/A204376/b204376.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*(78 - 24*x - 71*x^2 - 118*x^3 - 14*x^4 + 37*x^5 + 8*x^6 + 4*x^7) / ((1 - x)*(1 - x - x^2)*(1 + x + x^2)). - _Colin Barker_, Jun 07 2018

%e Some solutions for n=3:

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

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

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

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

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

%Y Cf. A204381.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 14 2012

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Last modified October 21 23:34 EDT 2021. Contains 348160 sequences. (Running on oeis4.)