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Number of (n+2)X(3+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 2 3 4 6 or 7 and every 3X3 column and antidiagonal sum not equal to 2 3 4 6 or 7
1

%I #4 Dec 17 2014 09:52:46

%S 983,774,1515,3302,8346,20998,50675,133296,343447,848007,2263089,

%T 5902801,14734098,39629269,104070383,261353804,706017540,1860981190,

%U 4689050899,12697106938,33535406222,84648673583,229505457761,606816472873

%N Number of (n+2)X(3+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 2 3 4 6 or 7 and every 3X3 column and antidiagonal sum not equal to 2 3 4 6 or 7

%C Column 3 of A252407

%H R. H. Hardin, <a href="/A252402/b252402.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 32*a(n-3) -310*a(n-6) +1291*a(n-9) -4641*a(n-12) +11713*a(n-15) -20535*a(n-18) +26754*a(n-21) -23045*a(n-24) +8109*a(n-27) +1127*a(n-30) -638*a(n-33) +162*a(n-36) -12*a(n-39) -7*a(n-42) +a(n-45) for n>48

%e Some solutions for n=4

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 17 2014