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

%I #4 Dec 16 2014 08:29:25

%S 185,300,588,948,2154,4702,7922,18772,41890,71050,169992,381820,

%T 648406,1556716,3506186,5956360,14322682,32301418,54882446,132071184,

%U 298048144,506441784,1219178902,2752229560,4676738148,11260602630,25424209614

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

%C Column 2 of A252278

%H R. H. Hardin, <a href="/A252272/b252272.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 17*a(n-3) -90*a(n-6) +188*a(n-9) -184*a(n-12) +89*a(n-15) -21*a(n-18) +2*a(n-21) for n>22

%e Some solutions for n=4

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 16 2014