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T(n,k)=1/4 the number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having at least two equal elements connected horizontally or vertically
10

%I #5 Mar 31 2012 12:35:56

%S 43,499,499,5695,17203,5695,65227,584143,584143,65227,746503,19882711,

%T 58656073,19882711,746503,8544883,676507975,5910714349,5910714349,

%U 676507975,8544883,97806031,23019453235,595270788529,1764076701091

%N T(n,k)=1/4 the number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having at least two equal elements connected horizontally or vertically

%C Table starts

%C .........43............499...............5695...................65227

%C ........499..........17203.............584143................19882711

%C .......5695.........584143...........58656073..............5910714349

%C ......65227.......19882711.........5910714349...........1764076701091

%C .....746503......676507975.......595270788529.........526180845527509

%C ....8544883....23019453235.....59956202692285......156962462690881921

%C ...97806031...783273204631...6038729388705523....46821946289531019895

%C .1119511003.26652142523719.608216983453837129.13967039613166010435737

%H R. H. Hardin, <a href="/A184153/b184153.txt">Table of n, a(n) for n = 1..84</a>

%e Some solutions for 4X3 with a(1,1)=0

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jan 09 2011