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T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having the absolute values of all six edge and diagonal differences no larger than 1
8

%I #4 Dec 19 2013 17:47:36

%S 31,145,145,673,1361,673,3127,12593,12593,3127,14527,116801,231713,

%T 116801,14527,67489,1082977,4279065,4279065,1082977,67489,313537,

%U 10041953,79003521,157630963,79003521,10041953,313537,1456615,93113761

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having the absolute values of all six edge and diagonal differences no larger than 1

%C Table starts

%C .......31.........145.............673...............3127.................14527

%C ......145........1361...........12593.............116801...............1082977

%C ......673.......12593..........231713............4279065..............79003521

%C .....3127......116801.........4279065..........157630963............5807422543

%C ....14527.....1082977........79003521.........5807422543..........427196005695

%C ....67489....10041953......1458813409.......214027901025........31446640848897

%C ...313537....93113761.....26937444801......7888454356625......2315408571668225

%C ..1456615...863396401....497411686793....290756314787875....170502665692732079

%C ..6767071..8005833073...9184935953377..10716964158533127..12556134956123911615

%C .31438129.74233997105.169604155276817.395017615132720993.924677153131389366689

%H R. H. Hardin, <a href="/A234122/b234122.txt">Table of n, a(n) for n = 1..364</a>

%F Empirical for column k:

%F k=1: a(n) = 4*a(n-1) +3*a(n-2)

%F k=2: a(n) = 10*a(n-1) -4*a(n-2) -26*a(n-3) +5*a(n-4)

%F k=3: a(n) = 20*a(n-1) -10*a(n-2) -324*a(n-3) -277*a(n-4) +144*a(n-5)

%F k=4: [order 11]

%F k=5: [order 17]

%F k=6: [order 35]

%F k=7: [order 62]

%e Some solutions for n=2 k=4

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

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

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

%Y Column 1 is A086901(n+3)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 19 2013