A221968 Number of -n..n arrays of length 5 with the sum ahead of each element differing from the sum following that element by n or less.

63, 705, 3647, 12609, 34111, 78273, 159615, 297857, 518719, 854721, 1345983, 2041025, 2997567, 4283329, 5976831, 8168193, 10959935, 14467777, 18821439, 24165441, 30659903, 38481345, 47823487, 58898049, 71935551, 87186113

Offset

1,1

Comments

Row 5 of A221967.

Links

R. H. Hardin, Table of n, a(n) for n = 1..63

Formula

Empirical: a(n) = (20/3)*n^5 + (50/3)*n^4 + 20*n^3 + (40/3)*n^2 + (16/3)*n + 1.

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

G.f.: x*(9 + 12*x - x^2)*(7 + 27*x + 5*x^2 + x^3) / (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=6:
.-5...-3...-4...-3....2...-2....6....4...-1....2....2....3...-6....0....1....5
..2....3....3....5...-1...-3...-4...-5...-2...-2....2...-2....5...-1....0...-6
.-1...-1....2....1...-1....4....6....3....2....1...-5...-4...-1...-1...-1....5
..2....6....0....1....2...-3...-5....1...-4....4....3....3...-4....0....2...-5
.-3...-3...-5...-2...-2...-1....5...-3...-2....1....3....1....1...-1....2....3

Crossrefs

Cf. A221967.

Sequence in context: A152725 A086578 A198399 * A115152 A343978 A284953

Adjacent sequences: A221965 A221966 A221967 * A221969 A221970 A221971

Keyword

nonn

Author

R. H. Hardin, Feb 01 2013

Status

approved