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%I #9 Apr 27 2018 06:28:46
%S 18,33,55,86,126,177,241,318,410,519,645,790,956,1143,1353,1588,1848,
%T 2135,2451,2796,3172,3581,4023,4500,5014,5565,6155,6786,7458,8173,
%U 8933,9738,10590,11491,12441,13442,14496,15603,16765,17984,19260,20595,21991
%N Number of nondecreasing arrangements of 4 numbers in -(n+2)..(n+2) with sum zero.
%C Row 4 of A188211.
%H R. H. Hardin, <a href="/A188212/b188212.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 3*a(n-4) + 3*a(n-5) - a(n-6).
%F Empirical g.f.: x*(18 - 21*x + 10*x^2 - 16*x^3 + 21*x^4 - 8*x^5) / ((1 - x)^4*(1 + x + x^2)). - _Colin Barker_, Apr 27 2018
%e Some solutions for n=3:
%e .-4...-5...-4...-5...-3...-1...-2...-2....0...-4...-3...-4...-2...-5...-4...-4
%e ..1...-1...-1....1...-2...-1...-2...-1....0...-1...-3...-3...-2...-3...-4...-2
%e ..1....2....1....2....0...-1....2....1....0....0....1....3....1....4....4....2
%e ..2....4....4....2....5....3....2....2....0....5....5....4....3....4....4....4
%Y Cf. A188211.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 24 2011
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