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

1,1

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)-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

Example

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

Crossrefs

Row 7 of A188122.

Sequence in context: A224954 A299131 A158479 * A189500 A350579 A075289

Adjacent sequences: A188123 A188124 A188125 * A188127 A188128 A188129

Keyword

nonn

Author

R. H. Hardin, Mar 21 2011

Status

approved