A188185 Number of strictly increasing arrangements of 7 numbers in -(n+5)..(n+5) with sum zero

94, 289, 734, 1656, 3370, 6375, 11322, 19138, 30982, 48417, 73316, 108108, 155646, 219489, 303748, 413442, 554256, 733005, 957332, 1236222, 1579666, 1999265, 2507780, 3119876, 3851588, 4721127, 5748298, 6955424, 8366614, 10008857

Offset

1,1

Comments

Row 7 of A188181

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).

Empirical: G.f. -x*(94 +101*x +156*x^2 +282*x^3 +347*x^4 +463*x^5 +423*x^6 +497*x^7 +393*x^8 +285*x^9 +180*x^10 +99*x^11 +17*x^12 -25*x^13 +47*x^14 -19*x^15 +25*x^16 +4*x^17 +22*x^18 -7*x^19 -44*x^20 +24*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 26 2011

Example

Some solutions for n=5
.-9...-7...-9..-10..-10..-10...-7...-9..-10..-10..-10..-10..-10...-9...-7..-10
.-7...-4...-7...-6...-7...-4...-6...-7...-3...-8...-5...-8...-8...-6...-6...-6
.-3...-2...-2...-5...-3...-3...-4...-4...-1...-2...-1...-7...-5...-1...-3...-5
.-1...-1....0....2....2...-1...-3....1....0...-1....1....3...-1....1...-2....1
..5....0....3....4....3....3....4....2....1....5....2....6....6....2....0....4
..6....6....6....7....6....7....7....8....4....7....4....7....8....4....8....7
..9....8....9....8....9....8....9....9....9....9....9....9...10....9...10....9

Crossrefs

Sequence in context: A116109 A107412 A115996 * A189811 A202415 A174337

Adjacent sequences: A188182 A188183 A188184 * A188186 A188187 A188188

Keyword

nonn

Author

R. H. Hardin Mar 23 2011

Status

approved