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A188125 Number of strictly increasing arrangements of 6 nonzero numbers in -(n+4)..(n+4) with sum zero. 1
4, 16, 52, 137, 308, 624, 1154, 1999, 3278, 5144, 7772, 11387, 16230, 22602, 30830, 41303, 54440, 70734, 90706, 114963, 144146, 178984, 220244, 268797, 325548, 391514, 467756, 555449, 655816, 770208, 900020, 1046787, 1212094, 1397668 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row 6 of A188122.

LINKS

R. H. Hardin, Table of n, a(n) for n = 0..200 (a(0) inserted by Georg Fischer, Jan 24 2019)

FORMULA

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)

= 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.

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

EXAMPLE

4 + 16*x + 52*x^2 + 137*x^3 + 308*x^4 + 624*x^5 + 1154*x^6 + 1999*x^7 + 3278*x^8 + ...

Some solutions for n=6

-10...-8...-7...-8...-8...-9...-9...-9...-9...-7..-10...-9...-7..-10...-9...-9

.-8...-6...-5...-5...-6...-3...-7...-3...-2...-5...-6...-5...-5...-6...-4...-5

.-1....1...-1...-1...-1...-2...-2....1...-1...-2...-2...-1...-1...-2...-2...-4

..4....3....1....1....2....3....3....2....1....1....2....1....3....3....1....3

..7....4....2....3....5....4....5....4....2....4....6....6....4....5....5....6

..8....6...10...10....8....7...10....5....9....9...10....8....6...10....9....9

PROG

(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 */

CROSSREFS

Cf. A188122

Sequence in context: A089093 A316321 A058234 * A007688 A320237 A197132

Adjacent sequences:  A188122 A188123 A188124 * A188126 A188127 A188128

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 21 2011

STATUS

approved

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Last modified December 7 20:44 EST 2019. Contains 329849 sequences. (Running on oeis4.)