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%I #4 Dec 11 2014 12:48:34
%S 1462,2255,2255,1933,1182,1933,2735,1251,1251,2735,4346,2053,2272,
%T 2053,4346,7115,3609,3572,3572,3609,7115,12344,7348,8756,8937,8756,
%U 7348,12344,20995,14434,21326,25231,25231,21326,14434,20995,36057,29212,47034,68456
%N T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum prime and every diagonal and antidiagonal sum nonprime
%C Table starts
%C ..1462...2255...1933....2735.....4346......7115......12344.......20995
%C ..2255...1182...1251....2053.....3609......7348......14434.......29212
%C ..1933...1251...2272....3572.....8756.....21326......47034......116348
%C ..2735...2053...3572....8937....25231.....68456.....177132......512051
%C ..4346...3609...8756...25231....87011....285399.....875435.....3103838
%C ..7115...7348..21326...68456...285399...1086474....3678858....15275433
%C .12344..14434..47034..177132...875435...3678858...14138322....70829204
%C .20995..29212.116348..512051..3103838..15275433...70829204...436167357
%C .36057..60954.285990.1394255.10096792..58358828..294856410..2122347433
%C .58580.125586.648986.3602453.31749014.199425794.1132100600.10131857942
%H R. H. Hardin, <a href="/A251950/b251950.txt">Table of n, a(n) for n = 1..509</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 41] for n>50
%F k=2: [order 21] for n>27
%F k=3: [order 30] for n>33
%F k=4: [order 36] for n>39
%F k=5: [order 54] for n>57
%F k=6: [order 66] for n>69
%F k=7: [order 90] for n>95
%e Some solutions for n=4 k=4
%e ..1..1..0..1..1..0....1..1..0..1..1..0....3..3..1..1..0..1....3..1..1..0..1..1
%e ..3..0..2..0..0..2....3..0..2..0..0..2....3..2..0..0..2..0....2..0..0..2..0..3
%e ..1..1..0..1..1..3....1..1..0..1..1..3....1..0..1..1..3..1....0..1..1..3..1..1
%e ..1..1..0..1..1..0....1..1..0..1..1..0....1..0..1..1..0..1....0..1..1..0..1..1
%e ..0..3..2..0..3..2....3..0..2..0..3..2....0..2..0..3..2..0....2..0..0..2..0..0
%e ..1..1..0..1..1..0....1..1..3..1..1..0....1..0..1..1..0..1....0..1..1..3..1..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 11 2014
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