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T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock summing to a prime
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%I #4 Dec 02 2014 18:36:37

%S 114,856,856,6398,12998,6398,47874,194586,194586,47874,358070,2922936,

%T 5783416,2922936,358070,2679006,43856564,172965058,172965058,43856564,

%U 2679006,20039054,658509724,5162094982,10325081994,5162094982,658509724

%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock summing to a prime

%C Table starts

%C ......114........856..........6398............47874..............358070

%C ......856......12998........194586..........2922936............43856564

%C .....6398.....194586.......5783416........172965058..........5162094982

%C ....47874....2922936.....172965058......10325081994........614533146306

%C ...358070...43856564....5162094982.....614533146306......72875563626720

%C ..2679006..658509724..154267520858...36647302556482....8664203110893480

%C .20039054.9883202426.4606843590302.2183158464447536.1028696788230851944

%H R. H. Hardin, <a href="/A251459/b251459.txt">Table of n, a(n) for n = 1..112</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 7]

%F k=2: [order 22]

%F k=3: [order 99]

%e Some solutions for n=2 k=4

%e ..0..2..0..2..1....0..2..1..0..1....0..2..1..0..0....0..2..0..0..0

%e ..0..0..0..0..0....0..0..0..2..2....0..0..0..2..1....0..0..0..2..3

%e ..3..2..0..2..1....0..3..0..1..2....1..2..1..2..0....3..0..3..0..0

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 02 2014