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T(n,k)=Number of (n+1)X(k+1) 0..5 arrays with every 2X2 subblock having the sum of the absolute values of all six edge and diagonal differences equal to 15
8

%I #4 Dec 21 2013 08:56:08

%S 104,440,440,1792,1732,1792,7584,6644,6644,7584,31552,28016,24480,

%T 28016,31552,133984,115680,104276,104276,115680,133984,560768,509536,

%U 429552,476804,429552,509536,560768,2386048,2169836,1961124,2064028,2064028

%N T(n,k)=Number of (n+1)X(k+1) 0..5 arrays with every 2X2 subblock having the sum of the absolute values of all six edge and diagonal differences equal to 15

%C Table starts

%C ......104.......440......1792.......7584.......31552......133984......560768

%C ......440......1732......6644......28016......115680......509536.....2169836

%C .....1792......6644.....24480.....104276......429552.....1961124.....8457288

%C .....7584.....28016....104276.....476804.....2064028....10399724....47733004

%C ....31552....115680....429552....2064028.....9242640....49998832...240124200

%C ...133984....509536...1961124...10399724....49998832...306674836..1604387244

%C ...560768...2169836...8457288...47733004...240124200..1604387244..8897304552

%C ..2386048...9814536..40227192..254130448..1384025392.10638242184.64901610764

%C .10017536..42498000.177596408.1198170996..6844958752.57639791844

%C .42680192.195663360.869944940.6642355444.41343086964

%H R. H. Hardin, <a href="/A234208/b234208.txt">Table of n, a(n) for n = 1..112</a>

%F Empirical for column k:

%F k=1: a(n) = 36*a(n-2) -396*a(n-4) +1392*a(n-6) -1664*a(n-8) +512*a(n-10)

%F k=2: [order 35]

%e Some solutions for n=3 k=4

%e ..1..4..0..2..0....2..5..2..5..1....5..2..0..5..2....4..4..4..0..4

%e ..0..4..5..2..5....1..5..1..5..2....0..2..5..5..1....1..0..5..4..1

%e ..1..4..0..2..0....0..1..0..1..5....2..5..1..2..5....4..4..4..0..4

%e ..0..4..5..2..5....5..1..5..1..4....0..2..5..5..1....0..1..0..3..0

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 21 2013