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A211478 Number of -1..1 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, two or three distinct values for every i<=n and j<=n. 1

%I #7 Jul 18 2018 07:47:20

%S 9,23,59,145,351,835,1971,4625,10831,25349,59387,139365,327791,772867,

%T 1826897,4329065,10282271,24474781,58370829,139453231,333678255,

%U 799483191,1917764183,4604847317,11066414301,26614313429,64046049399

%N Number of -1..1 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, two or three distinct values for every i<=n and j<=n.

%H R. H. Hardin, <a href="/A211478/b211478.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) - 15*a(n-2) + a(n-3) + 33*a(n-4) - 28*a(n-5) - 12*a(n-6) + 16*a(n-7) + a(n-8) - 2*a(n-9).

%F Empirical g.f.: x*(9 - 40*x + 33*x^2 + 68*x^3 - 99*x^4 - 13*x^5 + 51*x^6 + x^7 - 6*x^8) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x - x^2)*(1 - x - 2*x^2 + x^3)). - _Colin Barker_, Jul 18 2018

%e Some solutions for n=5:

%e ..0....1....0....0....1...-1....0....1....1....0....1...-1....1....0....1...-1

%e .-1...-1....0....1....0....0....0...-1...-1...-1....1....0....0....1....0....0

%e ..0....0...-1...-1...-1....1....1....0...-1....1....1....0....0....0....1...-1

%e .-1....0....0....0....0....0...-1....0...-1....1...-1....0....1...-1....0....1

%e ..0....0...-1....1....0...-1...-1....0...-1....1....0....1....0....0....0....1

%e ..0...-1....0...-1...-1....1...-1....0...-1....1...-1....0....1...-1....0...-1

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 12 2012

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