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T(n,k)=Number of length n+4 0..k arrays with every five consecutive terms having two times the sum of some three elements equal to three times the sum of the remaining two
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%I #6 Dec 12 2014 20:50:23

%S 2,53,2,204,53,2,585,204,53,2,1326,585,204,53,2,2817,1654,585,204,53,

%T 2,5028,4137,2042,585,204,53,2,8789,7964,6065,2494,585,204,53,2,13970,

%U 14661,12644,8873,3014,585,204,53,2,21601,23778,24583,20128,12937,3606

%N T(n,k)=Number of length n+4 0..k arrays with every five consecutive terms having two times the sum of some three elements equal to three times the sum of the remaining two

%C Table starts

%C .2.53.204.585.1326...2817...5028....8789...13970...21601....31512....45353

%C .2.53.204.585.1654...4137...7964...14661...23778...39441....60264....90193

%C .2.53.204.585.2042...6065..12644...24583...40878...72399...115668...180421

%C .2.53.204.585.2494...8873..20128...41419...70770..133223...222176...361717

%C .2.53.204.585.3014..12937..32094...70037..123076..245471...426828...726053

%C .2.53.204.585.3606..18737..51166..118685..214530..452471...819664..1457951

%C .2.53.204.585.4742..30017..86800..206989..376806..854053..1617708..2998849

%C .2.53.204.585.6130..47953.147582..362631..665532.1612155..3189728..6170069

%C .2.53.204.585.7782..76161.250880..637211.1180180.3039269..6274962.12677003

%C .2.53.204.585.9710.119849.425828.1122703.2100020.5721757.12312020.25999019

%H R. H. Hardin, <a href="/A248987/b248987.txt">Table of n, a(n) for n = 1..2166</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1)

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

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

%F k=4: a(n) = a(n-1)

%F k=5: [linear recurrence of order 21]

%F k=6: [order 51]

%F Empirical for row n:

%F n=1: [linear recurrence of order 12; also a polynomial of degree 4 plus a quadratic quasipolynomial with period 6]

%e Some solutions for n=6 k=4

%e ..2....2....2....1....2....2....1....3....2....2....3....3....1....2....4....4

%e ..0....4....4....1....0....1....1....2....3....0....2....2....4....2....0....4

%e ..0....2....4....3....4....1....2....4....1....4....1....3....3....3....4....2

%e ..1....0....3....4....4....4....3....1....4....3....2....0....4....1....2....1

%e ..2....2....2....1....0....2....3....0....0....1....2....2....3....2....0....4

%e ..2....2....2....1....2....2....1....3....2....2....3....3....1....2....4....4

%e ..0....4....4....1....0....1....1....2....3....0....2....2....4....2....0....4

%e ..0....2....4....3....4....1....2....4....1....4....1....3....3....3....4....2

%e ..1....0....3....4....4....4....3....1....4....3....2....0....4....1....2....1

%e ..2....2....2....1....0....2....3....0....0....1....2....2....3....2....0....4

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Oct 18 2014