A221969 Number of -n..n arrays of length 6 with the sum ahead of each element differing from the sum following that element by n or less.

129, 2305, 16513, 73089, 241153, 653185, 1535745, 3246337, 6316417, 11500545, 19831681, 32682625, 51833601, 79545985, 118642177, 172591617, 245602945, 342722305, 469937793, 634290049, 843988993, 1108536705, 1438856449

Offset

1,1

Comments

Row 6 of A221967.

Links

R. H. Hardin, Table of n, a(n) for n = 1..35

Formula

Empirical: a(n) = (128/15)*n^6 + (128/5)*n^5 + (112/3)*n^4 + 32*n^3 + (272/15)*n^2 + (32/5)*n + 1.

Conjectures from Colin Barker, Aug 14 2018: (Start)

G.f.: x*(3 + x)*(43 + 453*x + 878*x^2 + 170*x^3 - 9*x^4 + x^5) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

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

Crossrefs

Cf. A221967.

Sequence in context: A013955 A294302 A343509 * A036085 A000541 A023876

Adjacent sequences: A221966 A221967 A221968 * A221970 A221971 A221972

Keyword

nonn

Author

R. H. Hardin, Feb 01 2013

Status

approved