A188127 Number of strictly increasing arrangements of 8 nonzero numbers in -(n+6)..(n+6) with sum zero.

137, 484, 1398, 3528, 7970, 16547, 32035, 58595, 102113, 170844, 275878, 432018, 658432, 979785, 1427065, 2039067, 2863403, 3958322, 5393994, 7254686, 9640296, 12669003, 16479033, 21231771, 27113883, 34340884, 43159574, 53852210, 66739242

Offset: 1

Author

R. H. Hardin Mar 21 2011

Keywords

• nonn

Comments

Row 8 of A188122

Examples

			Some solutions for n=6
-12..-11..-12...-8..-10..-12...-9..-10...-6..-12...-8..-10..-12..-10..-12..-11
.-9..-10...-7...-7...-7..-11...-8...-8...-5...-9...-7...-6...-4...-8...-9...-7
.-8...-2...-6...-4...-4...-3...-7...-7...-2...-3...-3...-3...-3...-5...-7...-5
.-2....1...-2...-3...-3...-2...-6...-5...-1...-2...-1...-1....1...-3....2...-4
..5....2...-1....3...-2....1....1....4....1....1....1....1....2....1....4...-2
..7....3....5....4....5....4....6....7....2....4....3....2....3....5....5....8
..9....5...11....7...10...11...11....8....5...10....4....5....6....8....7....9
.10...12...12....8...11...12...12...11....6...11...11...12....7...12...10...12
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n)=2*a(n-1)-a(n-3)-a(n-5)+a(n-6)-a(n-7)+a(n-9)+a(n-10)+a(n-12)-2*a(n-13)-2*a(n-16)+a(n-17)+a(n-19)+a(n-20)-a(n-22)+a(n-23)-a(n-24)-a(n-26)+2*a(n-28)-a(n-29).

Empirical: G.f. -x*(-137 -210*x -3284*x^12 -869*x^3 -1398*x^4 -2142*x^5 -2816*x^6 -3546*x^7 -4084*x^8 -4269*x^10 -3951*x^11 -2644*x^13 -1892*x^14 -1202*x^15 -768*x^16 -389*x^17 -202*x^18 -87*x^19 -5*x^20 +20*x^21 -26*x^22 +32*x^23 +5*x^24 +29*x^25 -9*x^26 -57*x^27 +31*x^28 -4356*x^9 -430*x^2) / ( (x^2-x+1) *(x^5-1) *(x^7-1) *(x^2+1) *(1+x+x^2)^2 *(1+x)^3 *(x-1)^6 ). - R. J. Mathar, Mar 21 2011