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T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having the sum of the absolute values of the edge differences equal to 6
9

%I #4 Dec 14 2013 07:48:06

%S 100,716,716,4974,10544,4974,34996,150054,150054,34996,245244,2172148,

%T 4350820,2172148,245244,1721166,31361288,130732438,130732438,31361288,

%U 1721166,12073496,453376730,3912088926,8271515976,3912088926,453376730

%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having the sum of the absolute values of the edge differences equal to 6

%C Table starts

%C ......100.........716............4974..............34996................245244

%C ......716.......10544..........150054............2172148..............31361288

%C .....4974......150054.........4350820..........130732438............3912088926

%C ....34996.....2172148.......130732438.........8271515976..........523893377896

%C ...245244....31361288......3912088926.......523893377896........70397790661236

%C ..1721166...453376730....117571581104.....33375589770090......9557844830798770

%C .12073496..6552999568...3530630987208...2127910272105792...1299207938978711788

%C .84707304.94726474064.106103463522318.135782900234876140.176985122261187048412

%H R. H. Hardin, <a href="/A233635/b233635.txt">Table of n, a(n) for n = 1..144</a>

%F Empirical for column k:

%F k=1: a(n) = 5*a(n-1) +19*a(n-2) -27*a(n-3) -55*a(n-4) +37*a(n-5)

%F k=2: [order 19]

%F k=3: [order 63]

%e Some solutions for n=2 k=4

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 14 2013