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

%I #4 Dec 15 2014 07:28:03

%S 945,1440,2055,3341,5300,7973,13044,21238,32234,53032,87440,133042,

%T 218874,363938,553312,908558,1520436,2306990,3778274,6356426,9620954,

%U 15713012,26556444,40091976,65299770,110813364,166873308,271087620

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

%C Column 1 of A252192

%H R. H. Hardin, <a href="/A252185/b252185.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = -a(n-1) +14*a(n-3) +14*a(n-4) +a(n-5) -76*a(n-6) -77*a(n-7) -13*a(n-8) +199*a(n-9) +212*a(n-10) +65*a(n-11) -243*a(n-12) -308*a(n-13) -159*a(n-14) +65*a(n-15) +224*a(n-16) +202*a(n-17) +138*a(n-18) -64*a(n-19) -128*a(n-20) -128*a(n-21) +32*a(n-23) +32*a(n-24) for n>30

%e Some solutions for n=4

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 15 2014