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

%I #4 Dec 18 2014 07:21:16

%S 475,798,1783,2818,8354,21510,39689,125839,336794,629921,2053845,

%T 5597331,10478832,34721174,95598360,178987291,598478883,1657157188,

%U 3102740091,10426225275,28958128577,54219655326,182680987768,508211364604

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

%C Column 3 of A252523

%H R. H. Hardin, <a href="/A252518/b252518.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 32*a(n-3) -310*a(n-6) +1093*a(n-9) -1724*a(n-12) +1309*a(n-15) -476*a(n-18) +82*a(n-21) -5*a(n-24) for n>29

%e Some solutions for n=4

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 18 2014