A188125 - OEIS

%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