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T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 0 3 5 6 or 8 and every 3X3 column and antidiagonal sum not equal to 0 3 5 6 or 8
16

%I #4 Dec 19 2014 10:24:04

%S 614,1051,725,1717,1379,1042,3235,2815,2817,1635,6403,6019,7031,5304,

%T 3022,12421,13879,17762,15119,14435,5503,25137,31514,58239,43595,

%U 51614,37917,9927,50144,71856,156499,147592,174803,153189,75859,19165,99378

%N T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 0 3 5 6 or 8 and every 3X3 column and antidiagonal sum not equal to 0 3 5 6 or 8

%C Table starts

%C ...614....1051....1717.....3235......6403......12421.......25137........50144

%C ...725....1379....2815.....6019.....13879......31514.......71856.......170404

%C ..1042....2817....7031....17762.....58239.....156499......437805......1506801

%C ..1635....5304...15119....43595....147592.....433665.....1358948......4510703

%C ..3022...14435...51614...174803....814008....3108884....11582748.....52469568

%C ..5503...37917..153189...617798...4274586...18149682....82404422....571397644

%C ..9927...75859..342559..1597203..11003134...51303874...264208755...1700337789

%C .19165..213611.1193633..6498007..62184813..373181073..2251674722..20242422160

%C .36457..599753.3615116.23325496.344281115.2202127052.16173953810.233838315214

%C .66942.1195427.8087690.60375689.865035915.6156657609.51883573465.674994668281

%H R. H. Hardin, <a href="/A252615/b252615.txt">Table of n, a(n) for n = 1..545</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 25] for n>31

%F k=2: [order 24] for n>33

%F k=3: [order 30] for n>38

%F k=4: [order 27] for n>35

%F k=5: [order 30] for n>38

%F k=6: [order 48] for n>57

%F k=7: [order 39] for n>48

%F Empirical for row n:

%F n=1: [linear recurrence of order 61] for n>69

%F n=2: [order 49] for n>52

%F n=3: [order 45] for n>48

%F n=4: [order 54] for n>58

%F n=5: [order 72] for n>75

%e Some solutions for n=4 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 19 2014