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A204485 Number of (n+2) X 3 0..1 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically or nw-to-se diagonally exactly one way, and new values 0..1 introduced in row major order. 1

%I #7 Mar 01 2023 14:26:13

%S 72,214,610,1690,4664,12809,35172,96615,265372,728983,2002395,5500247,

%T 15108294,41499921,113994101,313124795,860106901,2362586936,

%U 6489676798,17826180446,48965883404,134502048011,369457236654,1014844430800

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

%C Column 1 of A204492.

%H R. H. Hardin, <a href="/A204485/b204485.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) -a(n-2) +4*a(n-3) -10*a(n-4) +18*a(n-6) -23*a(n-7) -3*a(n-9) +43*a(n-10) -86*a(n-11) +114*a(n-12) -85*a(n-13) +46*a(n-14) -16*a(n-15) -3*a(n-16) -4*a(n-17) +4*a(n-18) for n>19.

%e Some solutions for n=3

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

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

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

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

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

%Y Cf. A204492.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 15 2012

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Last modified April 24 20:08 EDT 2024. Contains 371963 sequences. (Running on oeis4.)