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A205257 Number of (n+2) X 3 0..1 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..1 introduced in row major order. 1

%I #8 Jun 11 2018 08:42:28

%S 240,1814,13728,103876,785920,5946280,44989988,340397184,2575465940,

%T 19486134776,147433307220,1115489560600,8439863289268,63856529812904,

%U 483142470500100,3655485938158424,27657633637846868,209259373825754344

%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, diagonally or antidiagonally, and new values 0..1 introduced in row major order.

%C Column 1 of A205264.

%H R. H. Hardin, <a href="/A205257/b205257.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) +7*a(n-2) +32*a(n-3) +34*a(n-4) +14*a(n-5) -20*a(n-6) -16*a(n-7).

%F Empirical g.f.: 2*x*(120 + 187*x + 582*x^2 + 565*x^3 + 180*x^4 - 352*x^5 - 256*x^6) / (1 - 6*x - 7*x^2 - 32*x^3 - 34*x^4 - 14*x^5 + 20*x^6 + 16*x^7). - _Colin Barker_, Jun 11 2018

%e Some solutions for n=3:

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

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

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

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

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

%Y Cf. A205264.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 24 2012

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Last modified July 18 10:00 EDT 2024. Contains 374378 sequences. (Running on oeis4.)