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%I #7 Mar 31 2012 12:36:12
%S 5142,11200,22563,42593,76251,130453,214784,341988,528926,797248,
%T 1174631,1695625,2403243,3350003,4599874,6229576,8330912,11012320,
%U 14401669,18648073,23925159,30433213,38402946,48097954,59819074,73907174,90748085
%N Number of nondecreasing arrangements of 8 nonzero numbers in -(n+6)..(n+6) with sum zero
%C Row 8 of A188333
%H R. H. Hardin, <a href="/A188338/b188338.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n)=2*a(n-1)-a(n-3)-a(n-5)+a(n-6)-a(n-7)+a(n-9)+a(n-10)+a(n-12)-2*a(n-13)-2*a(n-16)+a(n-17)+a(n-19)+a(n-20)-a(n-22)+a(n-23)-a(n-24)-a(n-26)+2*a(n-28)-a(n-29).
%F Empirical: G.f. -x*(-5142 -916*x -2609*x^3 -2265*x^4 -5656*x^5 -2529*x^6 -5176*x^7 -6633*x^8 -5259*x^9 -2576*x^10 +3400*x^12 -110*x^13 +1064*x^14 +3324*x^15 -2452*x^16 -1012*x^17 -2864*x^18 -1943*x^19 +601*x^20 +1598*x^21 -1297*x^22 +2352*x^23 +675*x^24 +1715*x^25 -1323*x^26 -3484*x^27 +2132*x^28 -2108*x^11 -163*x^2) / ( (x^2-x+1) *(x^4+x^3+x^2+x+1) *(x^6+x^5+x^4+x^3+x^2+x+1) *(x^2+1) *(1+x+x^2)^2 *(1+x)^3 *(x-1)^8 ). - R. J. Mathar, Mar 28 2011
%e Some solutions for n=6
%e -12..-12..-12...-6..-11...-9..-11..-11..-11..-11..-12...-9..-12..-12..-11..-12
%e .-9...-9..-10...-6...-7...-8...-4...-9..-10...-8...-8...-7...-7..-10..-10...-9
%e .-6...-6...-7...-5...-3...-8...-1...-8...-6...-2...-6...-5...-5...-8...-9...-9
%e .-4...-4...-4...-3....1...-2...-1...-3...-1...-2....3....2...-2...-6...-7...-7
%e ..1...-4....3...-2....4....5....2....1....4...-2....3....2....5....5....6....6
%e ..7...11....6....4....4....5....2....7....4....4....6....3....6...10....9....7
%e .11...12...12....9....6....6....6...11....8...10....7....7....6...10...11...12
%e .12...12...12....9....6...11....7...12...12...11....7....7....9...11...11...12
%K nonn
%O 1,1
%A _R. H. Hardin_ Mar 28 2011
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