A201814 Number of arrays of 6 integers in -n..n with sum zero and equal numbers of elements greater than zero and less than zero.

141, 1001, 4621, 15681, 42821, 99961, 207621, 394241, 697501, 1165641, 1858781, 2850241, 4227861, 6095321, 8573461, 11801601, 15938861, 21165481, 27684141, 35721281, 45528421, 57383481, 71592101, 88488961, 108439101, 131839241

Offset

1,1

Comments

Row 6 of A201811.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 11*n^5 + 65*n^3 + 64*n + 1.

Conjectures from Colin Barker, May 25 2018: (Start)

G.f.: x*(141 + 155*x + 730*x^2 + 150*x^3 + 145*x^4 - x^5) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

Some solutions for n=6:
..6....4....2...-5...-6....6....2...-2...-4...-4...-4....0....4...-4....5...-4
.-5....1....6...-1....2....5...-4...-4...-1....1...-3....5...-1....1...-3...-1
.-4...-4...-5....3....5....1...-2....0....3...-1....4...-4....3...-4...-5....4
..1...-2...-4....5...-1...-5....2....2...-6....6....1....0...-4...-1....5....1
.-1....4...-3...-4...-6...-5...-1....0....6....1...-3...-2...-6....2....2...-4
..3...-3....4....2....6...-2....3....4....2...-3....5....1....4....6...-4....4

Crossrefs

Cf. A201811.

Sequence in context: A068046 A186954 A235760 * A235543 A204469 A201553

Adjacent sequences: A201811 A201812 A201813 * A201815 A201816 A201817

Keyword

nonn

Author

R. H. Hardin, Dec 05 2011

Status

approved