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%I #7 Mar 31 2012 12:36:12
%S 40,86,166,288,472,726,1076,1534,2130,2878,3814,4954,6340,7990,9950,
%T 12242,14918,18000,21546,25582,30170,35338,41154,47648,54894,62924,
%U 71816,81606,92378,104168,117066,131112,146400,162972,180928,200312,221230
%N Number of nondecreasing arrangements of 5 nonzero numbers in -(n+3)..(n+3) with sum zero
%C Row 5 of A188333
%H R. H. Hardin, <a href="/A188335/b188335.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n)=2*a(n-1)-a(n-3)-2*a(n-5)+2*a(n-6)+a(n-8)-2*a(n-10)+a(n-11).
%F Empirical: g.f. -2*x*(20 +3*x -3*x^2 -2*x^3 -9*x^4 +14*x^5 +2*x^6 +7*x^7 -4*x^8 -12*x^9 +7*x^10) / ( (x^2+1) *(1+x+x^2) *(1+x)^2 *(x-1)^5 ). a(n) = 23*n^4/288 +175*n^3/144 +985*n^2/144 +1601*n/96 +25265/1728 -(-1)^n*(3*n/32+27/64) -2*A061347(n+1)/27 -A057077(n+1)/8. - R. J. Mathar, Mar 28 2011
%e Some solutions for n=6
%e .-4...-7...-4...-7...-5...-9...-6...-7...-5...-7...-9...-5...-9...-5...-8...-6
%e .-3...-3...-3...-4...-5...-7...-6...-4...-4...-4...-5...-4...-3...-3...-3...-6
%e ..1...-1...-3....2....1....1....2....2...-1....3....3....2....2....1...-2...-1
%e ..3....4....4....3....2....6....2....4....4....4....3....3....5....1....5....4
%e ..3....7....6....6....7....9....8....5....6....4....8....4....5....6....8....9
%K nonn
%O 1,1
%A _R. H. Hardin_ Mar 28 2011
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