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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 3 5 6 or 8 and every 3X3 diagonal and antidiagonal sum equal to 0 3 5 6 or 8
1

%I #4 Dec 16 2014 20:44:56

%S 1331,2864,6986,15208,42345,111519,294801,852023,2391671,6526332,

%T 19388874,55236910,154718356,459605140,1324410518,3750331025,

%U 11134189835,32227560268,92034892492,272465735794,791324270153,2272219351820

%N Number of (n+2)X(3+2) 0..3 arrays with every 3X3 subblock row and column sum not equal to 0 3 5 6 or 8 and every 3X3 diagonal and antidiagonal sum equal to 0 3 5 6 or 8

%C Column 3 of A252352

%H R. H. Hardin, <a href="/A252347/b252347.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) +4*a(n-2) +47*a(n-3) -51*a(n-4) -204*a(n-5) -568*a(n-6) +772*a(n-7) +3088*a(n-8) -559*a(n-9) -2529*a(n-10) -10116*a(n-11) +27893*a(n-12) -17777*a(n-13) -71108*a(n-14) -50056*a(n-15) +121164*a(n-16) +484656*a(n-17) -377388*a(n-18) -107268*a(n-19) -429072*a(n-20) +1113936*a(n-21) -684864*a(n-22) -2739456*a(n-23) +944928*a(n-24) +1794528*a(n-25) +7178112*a(n-26) -5705856*a(n-27) -1472256*a(n-28) -5889024*a(n-29) +5515776*a(n-30) +373248*a(n-31) +1492992*a(n-32) -1492992*a(n-33) for n>38

%e Some solutions for n=4

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 16 2014