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 A204641 Number of (n+2) X 9 0..3 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..3 introduced in row major order. 1

%I

%S 144255,8140,9750,8179,9482,16171,16636,40170,134630,418053,1557876,

%T 5894935,22113794,83799892,317716438,1203888543,4564208774,

%U 17304289587,65603583264,248721866374,942976402982,3575089125409,13554191367904

%N Number of (n+2) X 9 0..3 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..3 introduced in row major order.

%C Column 7 of A204642.

%H R. H. Hardin, <a href="/A204641/b204641.txt">Table of n, a(n) for n = 1..121</a>

%F Empirical: a(n) = 5*a(n-1) -3*a(n-2) -4*a(n-3) -12*a(n-4) +12*a(n-5) +21*a(n-6) -9*a(n-7) -9*a(n-8) for n>10.

%F Empirical g.f.: x*(144255 - 713135*x + 401815*x^2 + 560869*x^3 + 1761457*x^4 - 1601082*x^5 - 3013092*x^6 + 1151934*x^7 + 1230813*x^8 + 1476*x^9) / ((1 - x)*(1 - x - x^2)*(1 - 3*x - 3*x^2)*(1 - 3*x^3)). - _Colin Barker_, Jun 08 2018

%e Some solutions for n=3:

%e ..0..0..1..0..0..2..2..3..0....0..0..1..0..1..0..0..1..1

%e ..0..0..1..0..0..2..2..3..0....0..0..1..0..1..0..0..1..1

%e ..0..0..1..0..0..2..2..3..0....0..0..1..0..1..0..0..1..1

%e ..0..0..1..0..0..2..2..3..0....0..0..1..0..1..0..0..1..1

%e ..0..0..1..0..0..2..2..3..0....0..0..1..0..1..0..0..1..1

%Y Cf. A204642.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 17 2012

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Last modified December 3 04:53 EST 2021. Contains 349445 sequences. (Running on oeis4.)