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%I #4 Dec 01 2014 22:06:52
%S 71,571,571,4585,12457,4585,36825,271393,271393,36825,295759,5914339,
%T 16036923,5914339,295759,2375387,128887759,948010753,948010753,
%U 128887759,2375387,19077905,2808783981,56040713651,152031391763,56040713651
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock summing to 2 3 4 5 or 6
%C Table starts
%C .......71.........571............4585..............36825.................295759
%C ......571.......12457..........271393............5914339..............128887759
%C .....4585......271393........16036923..........948010753............56040713651
%C ....36825.....5914339.......948010753.......152031391763.........24381056748093
%C ...295759...128887759.....56040713651.....24381056748093......10607219852841053
%C ..2375387..2808783981...3312804237391...3909974244432939....4614802877342194801
%C .19077905.61210372853.195833921630923.627040122137369465.2007727783867224687619
%H R. H. Hardin, <a href="/A251390/b251390.txt">Table of n, a(n) for n = 1..161</a>
%F Empirical for column k:
%F k=1: a(n) = 8*a(n-1) +a(n-2) -6*a(n-3)
%F k=2: a(n) = 23*a(n-1) -21*a(n-2) -119*a(n-3) +66*a(n-4) +72*a(n-5) -32*a(n-6)
%F k=3: [order 15]
%F k=4: [order 40]
%e Some solutions for n=2 k=4
%e ..0..0..0..1..2....0..0..0..0..2....0..0..0..1..2....0..0..0..0..0
%e ..2..1..2..2..0....2..2..1..2..1....1..1..1..2..0....2..2..1..2..0
%e ..1..1..1..0..1....0..2..1..1..2....2..0..1..1..2....0..2..0..2..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 01 2014
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