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A211504 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, three or four distinct values for every i<=n and j<=n. 1

%I #8 Jul 18 2018 09:56:00

%S 48,330,2262,15474,105642,719838,4895886,33239874,225294570,

%T 1524529134,10300146510,69486664818,468097569162,3149005428126,

%U 21156149373582,141954447726498,951332764533354,6368070500470926,42578969613094542

%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, three or four distinct values for every i<=n and j<=n.

%H R. H. Hardin, <a href="/A211504/b211504.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 24*a(n-1) - 210*a(n-2) + 756*a(n-3) - 659*a(n-4) - 1164*a(n-5) - 390*a(n-6) - 36*a(n-7).

%F Empirical g.f.: 6*x*(8 - 137*x + 737*x^2 - 967*x^3 - 1427*x^4 - 460*x^5 - 42*x^6) / ((1 - 6*x)*(1 - 6*x - x^2)*(1 - 6*x - 2*x^2)*(1 - 6*x - 3*x^2)). - _Colin Barker_, Jul 18 2018

%e Some solutions for n=5:

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 13 2012

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