A221970 Number of -n..n arrays of length 7 with the sum ahead of each element differing from the sum following that element by n or less.

255, 7425, 73983, 419841, 1690623, 5407233, 14661375, 35111681, 76335103, 153588225, 290033151, 519482625, 889719039, 1466441985, 2337899007, 3620254209, 5463749375, 8059712257, 11648466687, 16528199169, 23064836607

Offset

1,1

Comments

Row 7 of A221967.

Links

R. H. Hardin, Table of n, a(n) for n = 1..31

Formula

Empirical: a(n) = (488/45)*n^7 + (1708/45)*n^6 + (2912/45)*n^5 + (602/9)*n^4 + (2072/45)*n^3 + (952/45)*n^2 + (32/5)*n + 1.

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

G.f.: x*(255 + 5385*x + 21723*x^2 + 21597*x^3 + 5469*x^4 + 219*x^5 + 9*x^6 - x^7) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

Example

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

Crossrefs

Cf. A221967.

Sequence in context: A258809 A321553 A321547 * A177897 A160913 A022190

Adjacent sequences: A221967 A221968 A221969 * A221971 A221972 A221973

Keyword

nonn

Author

R. H. Hardin, Feb 01 2013

Status

approved