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Number of -3..3 arrays x(i) of n+1 elements i=1..n+1 with x(i)+x(j), x(i+1)+x(j+1), -(x(i)+x(j+1)), and -(x(i+1)+x(j)) having two or three distinct values for every i<=n and j<=n
1

%I #4 Apr 13 2012 14:33:45

%S 48,130,298,660,1384,2890,5850,11930,23806,48056,95422,191866,380806,

%T 765090,1521180,3058882,6098874,12284898,24573634,49602712,99555058,

%U 201409462,405573782,822380214,1661216936,3375887170,6839392998

%N Number of -3..3 arrays x(i) of n+1 elements i=1..n+1 with x(i)+x(j), x(i+1)+x(j+1), -(x(i)+x(j+1)), and -(x(i+1)+x(j)) having two or three distinct values for every i<=n and j<=n

%H R. H. Hardin, <a href="/A211500/b211500.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) +13*a(n-2) -43*a(n-3) -67*a(n-4) +254*a(n-5) +171*a(n-6) -797*a(n-7) -213*a(n-8) +1427*a(n-9) +85*a(n-10) -1458*a(n-11) +60*a(n-12) +810*a(n-13) -58*a(n-14) -224*a(n-15) +12*a(n-16) +24*a(n-17)

%e Some solutions for n=5

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Apr 13 2012