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T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of the elements above it, modulo 4
14

%I #4 Mar 16 2014 12:50:23

%S 2,5,5,12,31,12,28,172,172,28,66,926,2187,926,66,156,5078,27341,27341,

%T 5078,156,368,27861,346028,790681,346028,27861,368,868,152260,4360887,

%U 22952323,22952323,4360887,152260,868,2048,832207,54774178,663249556

%N T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of the elements above it, modulo 4

%C Table starts

%C ....2.......5.........12.............28................66..................156

%C ....5......31........172............926..............5078................27861

%C ...12.....172.......2187..........27341............346028..............4360887

%C ...28.....926......27341.........790681..........22952323............663249556

%C ...66....5078.....346028.......22952323........1527488498.........101276030555

%C ..156...27861....4360887......663249556......101276030555.......15397080750829

%C ..368..152260...54774178....19117551262.....6693244281896.....2331550702010844

%C ..868..832207..688266175...550960518608...442014330398515...352742924096563362

%C .2048.4550810.8649330696.15873533676775.29178369838713161.53342694175522093768

%H R. H. Hardin, <a href="/A239340/b239340.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

%F k=2: [order 16]

%F k=3: [order 64]

%e Some solutions for n=3 k=4

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Mar 16 2014