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%I #18 Jan 24 2019 03:36:49
%S 4,16,52,137,308,624,1154,1999,3278,5144,7772,11387,16230,22602,30830,
%T 41303,54440,70734,90706,114963,144146,178984,220244,268797,325548,
%U 391514,467756,555449,655816,770208,900020,1046787,1212094,1397668
%N Number of strictly increasing arrangements of 6 nonzero numbers in -(n+4)..(n+4) with sum zero.
%C Row 6 of A188122.
%H R. H. Hardin, <a href="/A188125/b188125.txt">Table of n, a(n) for n = 0..200</a> (a(0) inserted by _Georg Fischer_, Jan 24 2019)
%F 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 = 168587/43200 +187*n/32 +3593*n^3/2160 +619*n^2/144 +457*n^4/1440 +11*n^5/450 -(-1)^n/64-3*n*(-1)^n/32 +4*(-1)^n*A119910(n+1)/27 -2*A117444(n+2)/25 +A057077(n)/8.
%F Empirical: G.f. -x*(-16 -20*x -33*x^2 -50*x^3 -60*x^4 -59*x^5 -51*x^6 -41*x^7 -18*x^8 -3*x^9 -x^10 +x^11 +4*x^12 -2*x^13 -7*x^14 +4*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 21 2011
%e 4 + 16*x + 52*x^2 + 137*x^3 + 308*x^4 + 624*x^5 + 1154*x^6 + 1999*x^7 + 3278*x^8 + ...
%e Some solutions for n=6
%e -10...-8...-7...-8...-8...-9...-9...-9...-9...-7..-10...-9...-7..-10...-9...-9
%e .-8...-6...-5...-5...-6...-3...-7...-3...-2...-5...-6...-5...-5...-6...-4...-5
%e .-1....1...-1...-1...-1...-2...-2....1...-1...-2...-2...-1...-1...-2...-2...-4
%e ..4....3....1....1....2....3....3....2....1....1....2....1....3....3....1....3
%e ..7....4....2....3....5....4....5....4....2....4....6....6....4....5....5....6
%e ..8....6...10...10....8....7...10....5....9....9...10....8....6...10....9....9
%o (PARI) {a(n) = local(v, c, m); m = n+4; forvec( v = vector( 6, i, [-m, m]), if( 0==prod( k=1, 6, v[k]), next); if( 0==sum( k=1, 6, v[k]), c++), 2); c} /* _Michael Somos_, Apr 11 2011 */
%Y Cf. A188122
%K nonn
%O 0,1
%A _R. H. Hardin_, Mar 21 2011
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