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
Keywords
Examples
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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..63
Crossrefs
Cf. A221967.
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)
Comments