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T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally at least two different ways, and new values 0..3 introduced in row major order
5

%I #5 Mar 31 2012 12:37:01

%S 900,15309,15309,296570,599534,296570,3885869,24722349,24722349,

%T 3885869,61395233,610123426,2434061311,610123426,61395233,998872022,

%U 19542294660,117341267705,117341267705,19542294660,998872022,15147453273

%N T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally at least two different ways, and new values 0..3 introduced in row major order

%C Table starts

%C ..........900..........15309..........296570..........3885869.........61395233

%C ........15309.........599534........24722349........610123426......19542294660

%C .......296570.......24722349......2434061311.....117341267705....7934236341512

%C ......3885869......610123426....117341267705....9238032333130.1101610965293914

%C .....61395233....19542294660...7934236341512.1101610965293914

%C ....998872022...640219515512.567813705120009

%C ..15147453273.19024434539826

%C .236632580900

%H R. H. Hardin, <a href="/A204320/b204320.txt">Table of n, a(n) for n = 1..40</a>

%e Some solutions for n=3 k=3

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jan 14 2012