A188126 Number of strictly increasing arrangements of 7 nonzero numbers in -(n+5)..(n+5) with sum zero.

42, 152, 426, 1032, 2216, 4376, 8044, 13994, 23210, 37030, 57086, 85506, 124816, 178186, 249308, 342708, 463550, 618042, 813186, 1057238, 1359422, 1730468, 2182232, 2728362, 3383832, 4165678, 5092482, 6185216, 7466594, 8962070

Offset: 1

Author

R. H. Hardin, Mar 21 2011

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Row 7 of A188122.

Formula

Empirical: a(n)=2*a(n-1)-a(n-3)-a(n-5)+a(n-6)-2*a(n-7)+2*a(n-8)+a(n-9)-a(n-13)-2*a(n-14)+2*a(n-15)-a(n-16)+a(n-17)+a(n-19)-2*a(n-21)+a(n-22) =

208637*n/12960 +413*(-1)^n/1152 +6403*n^3/1296 +355951*n^2/28800 +11*(-1)^n*n^2/384 +13*(-1)^n*n/96 +28669*n^4/25920 +709*n^5/5400 +841*n^6/129600 +6124649/777600 + (157*A049347(n)+74*A049347(n-1))/486 + 5*A128214(n+3)/81 +2*b(n)/25 + A057079(n+2)/18 -(-1)^(floor((n+1)/2))*A000034(n+1)/8 where b(n) is the 5-periodic sequence (-3,-1,-1,2,3,...) with offset 0.

Empirical: G.f. -2*x *(21 +34*x +61*x^2 +111*x^3 +152*x^4 +206*x^5 +217*x^6 +240*x^7 +212*x^8 +172*x^9 +120*x^10 +77*x^11 +36*x^12 +9*x^13 +11*x^14 -x^15 +4*x^16 +4*x^18 -8*x^20 +4*x^21) / ( (x^2-x+1) *(x^4+x^3+x^2+x+1) *(x^2+1) *(1+x+x^2)^2 *(1+x)^3 *(x-1)^7 ). - R. J. Mathar, Mar 21 2011