%I #4 Dec 10 2014 10:06:03

%S 5495,11492,11492,20025,16857,20025,49529,36085,36085,49529,117744,

%T 100787,94046,100787,117744,256604,242531,237142,237142,242531,256604,

%U 676969,725325,848547,1036785,848547,725325,676969,1694929,2472269

%N T(n,k)=Number of (n+2)X(k+2) 0..4 arrays with every 3X3 subblock row and column sum prime and every diagonal and antidiagonal sum nonprime

%C Table starts

%C .....5495....11492.....20025......49529......117744.......256604.........676969

%C ....11492....16857.....36085.....100787......242531.......725325........2472269

%C ....20025....36085.....94046.....237142......848547......2892699........8113568

%C ....49529...100787....237142....1036785.....4243461.....14269266.......64083601

%C ...117744...242531....848547....4243461....17612152.....96631623......513228578

%C ...256604...725325...2892699...14269266....96631623....615536028.....3186483082

%C ...676969..2472269...8113568...64083601...513228578...3186483082....27379339268

%C ..1694929..6408131..29479780..266275459..2133116461..21970640444...220952120769

%C ..3850641.19769560.102515893..902777675.12086844180.143585893407..1384444723597

%C .10168955.78452511.303454217.4085369642.67036259385.763905174081.11996291910088

%H R. H. Hardin, <a href="/A251885/b251885.txt">Table of n, a(n) for n = 1..199</a>

%e Some solutions for n=3 k=4

%e ..0..3..4..0..1..4....0..2..3..0..4..1....1..0..1..1..0..1....1..1..1..1..1..3

%e ..3..1..3..3..1..3....4..0..3..4..0..3....0..2..0..0..2..3....2..3..0..4..1..0

%e ..4..1..0..4..3..0....3..3..1..3..3..1....1..0..1..1..0..1....0..3..4..0..3..4

%e ..0..3..4..0..3..0....4..4..3..0..4..1....1..0..1..1..0..1....1..1..3..3..1..1

%e ..3..1..1..1..1..3....4..0..3..4..0..3....0..2..0..3..2..0....4..1..0..4..3..0

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 10 2014