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%I #9 May 20 2018 12:23:47
%S 12,68,186,422,798,1316,2064,3048,4254,5802,7682,9864,12500,15564,
%T 19010,23022,27558,32556,38232,44528,51366,58994,67338,76304,86172,
%U 96852,108234,120630,133934,148020,163232,179448,196526,214842,234258,254616
%N Number of -n..n arrays x(0..3) of 4 elements with zero sum and nonzero second and third differences.
%C Row 1 of A200204.
%H R. H. Hardin, <a href="/A200205/b200205.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) -4*a(n-4) +2*a(n-5) -a(n-6) +2*a(n-7) -a(n-8).
%F Empirical g.f.: 2*x*(6 + 22*x + 31*x^2 + 47*x^3 + 26*x^4 + 9*x^5 + 3*x^6) / ((1 - x)^4*(1 + x + x^2)^2). - _Colin Barker_, May 20 2018
%e Some solutions for n=3:
%e .-1....1....2....1...-3....2....2...-1....0....0....2....2....1...-2....1....1
%e ..3...-2....2...-1....1....2....2...-3...-2....3....0...-1....3....1...-3...-2
%e .-1....0...-1....3....3...-2...-3....2....3...-2...-3...-2...-3....0....1....3
%e .-1....1...-3...-3...-1...-2...-1....2...-1...-1....1....1...-1....1....1...-2
%Y Cf. A200204.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 14 2011
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