A201815 Number of arrays of 7 integers in -n..n with sum zero and equal numbers of elements greater than zero and less than zero.

393, 4145, 23857, 90609, 263201, 637393, 1355145, 2613857, 4675609, 7876401, 12635393, 19464145, 28975857, 41894609, 59064601, 81459393, 110191145, 146519857, 191862609, 247802801, 316099393, 398696145, 497730857, 615544609

Offset

1,1

Comments

Row 7 of A201811.

Links

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

Formula

Empirical: a(n) = 77*n^5 + 175*n^3 + 140*n + 1.

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

G.f.: x*(393 + 1787*x + 4882*x^2 + 1782*x^3 + 397*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=4.
..1....3....0....1....4...-4...-4....3...-2....0....2....2...-3....4....4....4
..2....1...-3...-1....3....4....1...-3....0....1...-3...-3....2....3...-3....1
..0...-3...-4...-2...-4....4....4...-3....1....4....0...-1...-3....0....0...-2
..4....0....4...-3...-4...-3...-3....3...-4...-2....2....1....0....2....0...-3
.-3...-2...-3....3....4....0....4....0....3...-1...-1....0....3...-3....0...-4
.-1...-2....2....2...-3....1....0...-1....4....1...-1...-3...-2...-2...-3....0
.-3....3....4....0....0...-2...-2....1...-2...-3....1....4....3...-4....2....4

Crossrefs

Cf. A201811.

Sequence in context: A083752 A047825 A227942 * A201554 A172636 A202046

Adjacent sequences: A201812 A201813 A201814 * A201816 A201817 A201818

Keyword

nonn

Author

R. H. Hardin, Dec 05 2011

Status

approved