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 A204367 Number of (n+2) X 7 0..2 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..2 introduced in row major order. 1

%I #9 Feb 16 2018 10:20:44

%S 2419,1715,1042,1264,1984,3280,7376,18776,48392,130552,355336,966472,

%T 2638568,7207496,19684040,53775496,146916424,401370184,1096560584,

%U 2995858760,8184813896,22361322568,61092269896,166907137864,455998772552

%N Number of (n+2) X 7 0..2 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..2 introduced in row major order.

%C Column 5 of A204370.

%H R. H. Hardin, <a href="/A204367/b204367.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) -6*a(n-4) +4*a(n-6) for n>9.

%F Empirical g.f.: x*(2419 - 5542*x - 4103*x^2 - 1862*x^3 + 12706*x^4 + 7618*x^5 - 5888*x^6 - 2628*x^7 - 200*x^8) / ((1 - x)*(1 - 2*x - 2*x^2)*(1 - 2*x^3)). - _Colin Barker_, Feb 16 2018

%e Some solutions for n=5:

%e ..0..0..1..1..1..0..1....0..0..1..1..1..0..1....0..1..2..2..1..1..2

%e ..0..0..0..1..1..1..2....0..0..0..1..1..1..2....0..1..2..2..1..1..1

%e ..1..0..0..0..1..1..1....2..0..0..0..1..1..1....0..1..2..2..1..1..2

%e ..1..1..0..0..0..1..1....2..2..0..0..0..1..1....0..1..2..2..1..1..2

%e ..1..1..1..0..0..0..1....2..2..2..0..0..0..1....0..1..2..2..1..1..2

%e ..0..1..1..1..0..0..0....0..2..2..2..0..0..0....0..1..2..2..1..1..2

%e ..0..2..1..1..1..0..0....2..0..2..2..2..0..0....0..1..2..2..1..1..2

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 14 2012

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Last modified May 29 17:26 EDT 2023. Contains 363042 sequences. (Running on oeis4.)