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%I #7 Mar 31 2012 12:36:11
%S 289,910,2430,5744,12346,24591,46029,81805,139143,227930,361384,
%T 556834,836618,1229093,1769773,2502617,3481445,4771508,6451232,
%U 8614108,11370764,14851235,19207395,24615603,31279561,39433366,49344790,61318804,75701312
%N Number of strictly increasing arrangements of 8 numbers in -(n+6)..(n+6) with sum zero
%C Row 8 of A188181
%H R. H. Hardin, <a href="/A188186/b188186.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n)=3*a(n-1)-2*a(n-2)-3*a(n-4)+4*a(n-5)-3*a(n-8)+3*a(n-9)-a(n-11)-a(n-12)+3*a(n-14)-3*a(n-15)+4*a(n-18)-3*a(n-19)-2*a(n-21)+3*a(n-22)-a(n-23).
%F Empirical: G.f. -x*(-289 -43*x -278*x^2 -274*x^3 -841*x^4 -615*x^5 -598*x^6 -412*x^7 -715*x^8 -363*x^9 -163*x^10 -72*x^11 -98*x^12 -200*x^13 +217*x^14 -5*x^15 -49*x^16 -253*x^17 +221*x^18 +23*x^19 +108*x^20 -206*x^21 +73*x^22) / ( (1+x) *(x^4+x^3+x^2+x+1) *(x^6+x^5+x^4+x^3+x^2+x+1) *(1+x+x^2)^2 *(x-1)^8 ). - R. J. Mathar, Mar 26 2011
%e Some solutions for n=5
%e .-9..-10..-10...-8..-11...-8...-9..-11...-9..-11..-11...-9..-11..-10..-10...-9
%e .-8...-8...-9...-7...-3...-5...-8..-10...-8...-7...-5...-7...-4...-9...-9...-7
%e .-5...-4...-7...-6...-2...-4...-5...-2...-6...-6...-4...-5...-3...-7...-7...-4
%e .-1....1....0...-2...-1...-3...-4....1...-1...-3...-3...-2...-2...-1....0...-1
%e ..1....2....2....0....1....0...-2....2....3....2....0....0....2....4....4....0
%e ..3....5....6....5....3....5....7....3....4....6....4....3....5....5....5....2
%e ..9....6....8....7....5....6...10....6....7....9....8....9....6....7....6....9
%e .10....8...10...11....8....9...11...11...10...10...11...11....7...11...11...10
%K nonn
%O 1,1
%A _R. H. Hardin_ Mar 23 2011
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