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A188336 Number of nondecreasing arrangements of 6 nonzero numbers in -(n+4)..(n+4) with sum zero.

%I A188336 #9 Jul 22 2025 11:08:45
%S A188336 197,424,828,1488,2519,4050,6252,9314,13479,19008,26224,35472,47169,
%T A188336 61756,79754,101712,128267,160088,197940,242622,295041,356138,426970,
%U A188336 508634,602351,709384,831128,969024,1124655,1299652,1495796,1714918
%N A188336 Number of nondecreasing arrangements of 6 nonzero numbers in -(n+4)..(n+4) with sum zero.
%C A188336 Row 6 of A188333
%H A188336 R. H. Hardin, <a href="/A188336/b188336.txt">Table of n, a(n) for n = 1..200</a>
%F A188336 Empirical: a(n)=2*a(n-1)-a(n-3)-a(n-5)+2*a(n-8)-a(n-11)-a(n-13)+2*a(n-15)-a(n-16).
%F A188336 Empirical: G.f. -x*(-197 -30*x +20*x^2 -29*x^3 +33*x^4 -37*x^5 -64*x^6 -157*x^7 +5*x^8 +27*x^9 +84*x^10 +24*x^11 +67*x^12 -46*x^13 -130*x^14 +78*x^15) / ( (1+x+x^2) *(x^4+x^3+x^2+x+1) *(x^2+1) *(1+x)^2 *(x-1)^6 ). - R. J. Mathar, Mar 28 2011
%e A188336 Some solutions for n=6
%e A188336 -10..-10...-3...-9...-7...-9...-9...-6...-7...-5...-7...-4...-6...-5...-9...-9
%e A188336 .-4...-6...-2...-3...-6...-1...-9...-6...-5...-4...-3...-3...-2...-5...-8...-7
%e A188336 ..1...-1...-2...-1...-2...-1...-4....1...-5...-4...-1...-1...-2...-2...-2....2
%e A188336 ..2....5....1...-1....1...-1....4....1....4....2....2....2....3...-2....4....3
%e A188336 ..4....5....3....4....4....6....9....4....5....4....4....3....3....6....5....4
%e A188336 ..7....7....3...10...10....6....9....6....8....7....5....3....4....8...10....7
%K A188336 nonn
%O A188336 1,1
%A A188336 _R. H. Hardin_ Mar 28 2011