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%I #4 Dec 02 2014 19:16:51
%S 114,586,586,2908,3904,2908,12670,24182,24182,12670,54344,123739,
%T 183485,123739,54344,218854,609565,1096596,1096596,609565,218854,
%U 874280,2696488,6216665,7485767,6216665,2696488,874280,3378058,11697274,30592799
%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock summing to a prime and those sums nondecreasing in every row and column
%C Table starts
%C ......114.......586........2908........12670........54344.......218854
%C ......586......3904.......24182.......123739.......609565......2696488
%C .....2908.....24182......183485......1096596......6216665.....30592799
%C ....12670....123739.....1096596......7485767.....48046512....261990105
%C ....54344....609565.....6216665.....48046512....347024304...2095872247
%C ...218854...2696488....30592799....261990105...2095872247..13874159417
%C ...874280..11697274...146035292...1374831443..12096838874..87400242458
%C ..3378058..47575204...638001419...6492635940..62069543650.484930994600
%C .12982168.191527226..2737224051..29922945960.308909778915
%C .48990334.740673411.11079334278.128376366657
%H R. H. Hardin, <a href="/A251481/b251481.txt">Table of n, a(n) for n = 1..97</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 16]
%F k=2: [order 61]
%F k=3: [order 99]
%e Some solutions for n=3 k=4
%e ..0..2..1..1..0....0..0..0..2..0....0..0..0..1..1....2..2..0..1..2
%e ..1..0..0..1..3....1..2..3..0..3....2..1..2..2..1....1..0..3..1..3
%e ..2..0..3..1..0....0..0..0..2..2....0..0..0..1..1....2..2..0..1..2
%e ..1..0..0..3..3....3..2..3..0..3....1..2..1..3..0....1..2..3..3..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 02 2014