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A211499 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 one or three distinct values for every i<=n and j<=n. 1

%I

%S 39,97,207,429,869,1733,3449,6815,13487,26619,52629,104001,205793,

%T 407403,807279,1600955,3176941,6309945,12537913,24933779,49598943,

%U 98736499,196590789,391673497,780437073,1555911947,3102177679,6187923707

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

%H R. H. Hardin, <a href="/A211499/b211499.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + 6*a(n-2) - 23*a(n-3) - 9*a(n-4) + 62*a(n-5) - 2*a(n-6) - 74*a(n-7) + 10*a(n-8) + 40*a(n-9) - 4*a(n-10) - 8*a(n-11).

%F Empirical g.f.: x*(39 - 20*x - 318*x^2 + 123*x^3 + 922*x^4 - 232*x^5 - 1170*x^6 + 164*x^7 + 632*x^8 - 40*x^9 - 120*x^10) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 4*x^2 + 2*x^4)). - _Colin Barker_, Jul 18 2018

%e Some solutions for n=5:

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 13 2012

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Last modified August 8 12:09 EDT 2022. Contains 356009 sequences. (Running on oeis4.)