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%I #4 Dec 10 2014 09:20:17
%S 1038,2146,2146,3092,5632,3092,5756,7160,7160,5756,11008,15116,7080,
%T 15116,11008,18400,36852,9936,9936,36852,18400,32372,41816,18464,
%U 13152,18464,41816,32372,60292,99808,31296,31520,31520,31296,99808,60292
%N T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum not 2 4 5 or 7 and every diagonal and antidiagonal sum 2 4 5 or 7
%C Table starts
%C ...1038...2146...3092...5756...11008...18400....32372....60292....100612
%C ...2146...5632...7160..15116...36852...41816....99808...169196....246152
%C ...3092...7160...7080...9936...18464...31296....40816....93176....140408
%C ...5756..15116...9936..13152...31520...46464....62720...164480....252736
%C ..11008..36852..18464..31520..107040..151704...267872...924272...1402224
%C ..18400..41816..31296..46464..151704..309144...506656..1847872...4274816
%C ..32372..99808..40816..62720..267872..506656...893120..3499888...8000000
%C ..60292.169196..93176.164480..924272.1847872..3499888.19032128..47257792
%C .100612.246152.140408.252736.1402224.4274816..8000000.47257792.165273152
%C .176372.568040.223728.389376.2561696.7487600.15317248.93188992.341663728
%H R. H. Hardin, <a href="/A251876/b251876.txt">Table of n, a(n) for n = 1..337</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 18] for n>23
%F k=2: [order 27] for n>33
%F k=3: a(n) = 15*a(n-3) -50*a(n-6) -160*a(n-9) +1056*a(n-12) -1280*a(n-15) for n>22
%F k=4: a(n) = 8*a(n-3) +16*a(n-6) -128*a(n-9) for n>17
%F k=5: a(n) = 21*a(n-3) -88*a(n-6) -336*a(n-9) +1664*a(n-12) for n>21
%F k=6: [order 18] for n>28
%F k=7: a(n) = 29*a(n-3) -168*a(n-6) for n>17
%e Some solutions for n=4 k=4
%e ..1..1..1..1..1..1....2..2..2..2..2..2....0..3..0..3..0..0....2..1..3..2..1..0
%e ..0..1..0..2..1..0....3..2..3..1..2..3....1..3..2..1..0..2....0..0..3..0..3..0
%e ..0..1..2..3..1..2....3..2..1..0..2..1....2..0..1..2..3..1....1..2..3..1..2..0
%e ..1..1..1..1..1..1....2..2..2..2..2..2....3..3..3..0..3..0....2..1..0..2..1..3
%e ..2..1..3..2..1..3....1..2..0..1..2..3....1..0..2..1..3..2....3..3..3..3..0..0
%e ..0..1..2..0..1..2....0..2..1..3..2..1....2..0..1..2..0..1....1..2..0..1..2..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 10 2014
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