A188213 Number of nondecreasing arrangements of 6 numbers in -(n+4)..(n+4) with sum zero.

338, 676, 1242, 2137, 3486, 5444, 8196, 11963, 17002, 23612, 32134, 42955, 56512, 73294, 93844, 118765, 148718, 184430, 226694, 276373, 334402, 401792, 479632, 569093, 671430, 787986, 920192, 1069575, 1237756, 1426456, 1637498, 1872809

Offset

1,1

Comments

Row 6 of A188211.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + 2*a(n-5) - a(n-6) - a(n-7) + 2*a(n-8) - a(n-10) - 2*a(n-11) + 3*a(n-12) - a(n-13).

Empirical g.f.: x*(338 - 338*x - 110*x^2 + 101*x^3 + 235*x^4 - 174*x^5 - 41*x^6 + 279*x^7 - 83*x^8 - 217*x^9 - 146*x^10 + 395*x^11 - 151*x^12) / ((1 - x)^6*(1 + x)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Apr 27 2018

Example

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

Crossrefs

Cf. A188211.

Sequence in context: A066478 A261707 A202443 * A250802 A186052 A186044

Adjacent sequences: A188210 A188211 A188212 * A188214 A188215 A188216

Keyword

nonn

Author

R. H. Hardin, Mar 24 2011

Status

approved