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%I #7 Dec 18 2014 07:26:59
%S 806,791,791,475,432,475,660,798,798,660,1093,1169,1783,1169,1093,
%T 1471,2492,2818,2818,2492,1471,2176,5214,8354,5628,8354,5214,2176,
%U 3809,9069,21510,17804,17804,21510,9069,3809,6101,20926,39689,47308,74181,47308
%N T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum not equal to 0 2 4 6 or 7 and every 3X3 diagonal and antidiagonal sum equal to 0 2 4 6 or 7
%C Table starts
%C ..806...791....475.....660.....1093......1471......2176.......3809........6101
%C ..791...432....798....1169.....2492......5214......9069......20926.......45114
%C ..475...798...1783....2818.....8354.....21510.....39689.....125839......336794
%C ..660..1169...2818....5628....17804.....47308.....96659.....310987......832766
%C .1093..2492...8354...17804....74181....268555....581529....2449868.....9015835
%C .1471..5214..21510...47308...268555...1215491...2662952...15755867....73792188
%C .2176..9069..39689...96659...581529...2662952...6486931...38674076...177771524
%C .3809.20926.125839..310987..2449868..15755867..38674076..304232630..1994599334
%C .6101.45114.336794..832766..9015835..73792188.177771524.1994599334.16970081459
%C .9098.80515.629921.1703099.19533141.160605830.432970668.4886570340.40415827217
%H R. H. Hardin, <a href="/A252523/b252523.txt">Table of n, a(n) for n = 1..544</a>
%F Empirical for column k:
%F k=1: a(n) = 6*a(n-3) -7*a(n-6) +2*a(n-9) for n>14
%F k=2: [order 21] for n>24
%F k=3: [order 24] for n>29
%F k=4: a(n) = 21*a(n-3) -62*a(n-6) +47*a(n-9) -5*a(n-12) for n>17
%F k=5: [order 36] for n>39
%F k=6: [order 42] for n>50
%F k=7: [order 21] for n>29
%e Some solutions for n=4 k=4
%e ..2..0..3..2..3..3....3..0..0..3..2..3....3..0..2..3..3..2....3..2..3..3..2..3
%e ..1..2..2..1..2..2....2..1..2..2..1..2....0..3..2..3..0..0....3..2..3..0..2..3
%e ..2..3..3..2..3..3....3..2..3..0..2..3....2..2..1..2..2..1....2..1..2..2..1..2
%e ..2..0..3..2..0..3....3..2..3..3..2..3....3..3..2..0..3..2....3..2..3..3..2..3
%e ..1..2..2..1..2..2....2..1..2..2..1..2....3..3..2..3..3..2....3..2..0..3..2..0
%e ..2..3..3..2..3..3....3..2..0..3..2..3....2..2..1..2..2..1....2..1..2..2..1..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 18 2014