A203290 Number of arrays of 2n nondecreasing integers in -7..7 with sum zero and equal numbers greater than zero and less than zero

8, 80, 580, 3172, 13934, 51768, 168314, 491187, 1310474, 3241912, 7518232, 16487840, 34435060, 68887342, 132636714, 246789735, 445262312, 781274626, 1336560456, 2234216814, 3656356722, 5868037410, 9249277184, 14337411833

Offset

1,1

Comments

Column 7 of A203291

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -2*a(n-5) +4*a(n-6) -4*a(n-7) +6*a(n-8) -6*a(n-9) -5*a(n-10) +4*a(n-11) +a(n-12) +2*a(n-13) +12*a(n-15) -17*a(n-16) +2*a(n-17) -2*a(n-18) +2*a(n-20) -2*a(n-21) +17*a(n-22) -12*a(n-23) -2*a(n-25) -a(n-26) -4*a(n-27) +5*a(n-28) +6*a(n-29) -6*a(n-30) +4*a(n-31) -4*a(n-32) +2*a(n-33) -4*a(n-34) +2*a(n-35) +4*a(n-36) -4*a(n-37) +a(n-38)

Example

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

Crossrefs

Sequence in context: A055346 A159710 A271555 * A100472 A043035 A165760

Adjacent sequences: A203287 A203288 A203289 * A203291 A203292 A203293

Keyword

nonn

Author

R. H. Hardin Dec 31 2011

Status

approved