A188334 Number of nondecreasing arrangements of 4 nonzero numbers in -(n+2)..(n+2) with sum zero

10, 20, 37, 61, 94, 136, 191, 257, 338, 434, 547, 677, 828, 998, 1191, 1407, 1648, 1914, 2209, 2531, 2884, 3268, 3685, 4135, 4622, 5144, 5705, 6305, 6946, 7628, 8355, 9125, 9942, 10806, 11719, 12681, 13696, 14762, 15883, 17059, 18292, 19582, 20933, 22343

Offset

1,1

Comments

Row 4 of A188333

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-4)+2*a(n-6)-a(n-7).

Empirical: -x*(-10+3*x^2+3*x^3-2*x^4-5*x^5+3*x^6) / ( (1+x)*(1+x+x^2)*(x-1)^4 ). a(n) = n^5/15-5*n^4/6+35*n^3/9-5*n^2 +253*n/30 +29/9 -2*A049347(n)/9. - R. J. Mathar, Mar 28 2011

Example

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

Crossrefs

Sequence in context: A046285 A048030 A048011 * A266087 A047881 A172172

Adjacent sequences: A188331 A188332 A188333 * A188335 A188336 A188337

Keyword

nonn

Author

R. H. Hardin Mar 28 2011

Status

approved