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A188334 Number of nondecreasing arrangements of 4 nonzero numbers in -(n+2)..(n+2) with sum zero.

%I A188334 #9 Jul 22 2025 11:08:30
%S A188334 10,20,37,61,94,136,191,257,338,434,547,677,828,998,1191,1407,1648,
%T A188334 1914,2209,2531,2884,3268,3685,4135,4622,5144,5705,6305,6946,7628,
%U A188334 8355,9125,9942,10806,11719,12681,13696,14762,15883,17059,18292,19582,20933,22343
%N A188334 Number of nondecreasing arrangements of 4 nonzero numbers in -(n+2)..(n+2) with sum zero.
%C A188334 Row 4 of A188333
%H A188334 R. H. Hardin, <a href="/A188334/b188334.txt">Table of n, a(n) for n = 1..200</a>
%F A188334 Empirical: a(n)=2*a(n-1)-a(n-3)-a(n-4)+2*a(n-6)-a(n-7).
%F A188334 Empirical: -x*(-10+3*x^2+3*x^3-2*x^4-5*x^5+3*x^6) / ( (1+x)*(1+x+x^2)*(x-1)^4 ). a(n) = n^5/15-5*n^4/6+35*n^3/9-5*n^2 +253*n/30 +29/9 -2*A049347(n)/9. - R. J. Mathar, Mar 28 2011
%e A188334 Some solutions for n=6
%e A188334 .-6...-7...-6...-8...-4...-2...-5...-8...-6...-5...-5...-4...-6...-4...-8...-4
%e A188334 ..1...-5...-1...-5...-3...-2...-5....1...-6....1...-2...-4...-3...-3...-3...-3
%e A188334 ..2....5...-1....6....2...-1....4....2....6....1...-1....4....4....3....4....1
%e A188334 ..3....7....8....7....5....5....6....5....6....3....8....4....5....4....7....6
%K A188334 nonn
%O A188334 1,1
%A A188334 _R. H. Hardin_ Mar 28 2011