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%I #4 Dec 15 2014 07:33:21
%S 945,1440,1440,2055,1886,2055,3341,2610,2610,3341,5300,3996,3705,3996,
%T 5300,7973,6368,5460,5460,6368,7973,13044,9508,8945,9233,8945,9508,
%U 13044,21238,15094,13737,14130,14130,13737,15094,21238,32234,24092,20974,21417
%N T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum equal to 0 1 3 6 or 7 and every 3X3 diagonal and antidiagonal sum not equal to 0 1 3 6 or 7
%C Table starts
%C ...945..1440..2055...3341...5300...7973..13044...21238...32234...53032....87440
%C ..1440..1886..2610...3996...6368...9508..15094...24092...36352...58610....94310
%C ..2055..2610..3705...5460...8945..13737..20974...34209...53194...82196...134418
%C ..3341..3996..5460...9233..14130..21417..34532...55336...84332..135776...218896
%C ..5300..6368..8945..14130..24956..37035..57284...99128..151616..245908...420808
%C ..7973..9508.13737..21417..37035..57629..87230..150297..239980..380896...661172
%C .13044.15094.20974..34532..57284..87230.147696..246676..385720..640208..1157336
%C .21238.24092.34209..55336..99128.150297.246676..488200..772384.1382480..3132872
%C .32234.36352.53194..84332.151616.239980.385720..772384.1339760.2298824..5554000
%C .53032.58610.82196.135776.245908.380896.640208.1382480.2298824.4201296.12409744
%H R. H. Hardin, <a href="/A252192/b252192.txt">Table of n, a(n) for n = 1..449</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 24] for n>30
%F k=2: a(n) = 7*a(n-3) -14*a(n-6) +8*a(n-9) for n>16
%F k=3: a(n) = 7*a(n-3) -14*a(n-6) +8*a(n-9) for n>15
%F k=4: a(n) = 7*a(n-3) -14*a(n-6) +8*a(n-9) for n>17
%F k=5: a(n) = 15*a(n-3) -70*a(n-6) +120*a(n-9) -64*a(n-12) for n>22
%F k=6: a(n) = 15*a(n-3) -70*a(n-6) +120*a(n-9) -64*a(n-12) for n>21
%F k=7: a(n) = 15*a(n-3) -70*a(n-6) +120*a(n-9) -64*a(n-12) for n>23
%e Some solutions for n=4 k=4
%e ..3..1..2..3..1..2....3..3..0..3..3..0....3..2..1..3..2..1....2..0..1..2..0..1
%e ..0..0..3..0..0..0....1..2..0..1..2..3....0..1..2..3..1..2....0..0..3..3..0..3
%e ..3..2..1..0..2..1....2..1..0..2..1..3....0..3..0..0..0..0....1..3..2..1..0..2
%e ..0..1..2..3..1..2....3..3..0..0..0..0....0..2..1..3..2..1....2..3..1..2..0..1
%e ..3..3..0..0..0..3....1..2..3..1..2..0....3..1..2..0..1..0....3..0..0..0..0..3
%e ..3..2..1..3..2..1....2..2..3..2..1..0....3..0..3..0..3..0....1..0..2..1..3..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 15 2014
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