A199899 Number of -n..n arrays x(0..3) of 4 elements with zero sum, and adjacent elements not both strictly positive and not both strictly negative.
15, 49, 111, 209, 351, 545, 799, 1121, 1519, 2001, 2575, 3249, 4031, 4929, 5951, 7105, 8399, 9841, 11439, 13201, 15135, 17249, 19551, 22049, 24751, 27665, 30799, 34161, 37759, 41601, 45695, 50049, 54671, 59569, 64751, 70225, 75999, 82081, 88479, 95201
Offset: 1
Keywords
Examples
Some solutions for n=6: ..3....3....4...-2....5...-2....5...-3....4...-3....0....2....0....6....3....1 ..0...-6...-4....6...-4....1...-5....2...-5....6....2...-2....5...-1...-5...-5 ..2....3....1...-6....3...-4....3...-1....5....0....0....5...-5....0....6....0 .-5....0...-1....2...-4....5...-3....2...-4...-3...-2...-5....0...-5...-4....4
Links
- R. H. Hardin, Table of n, a(n) for n = 1..200
Crossrefs
Cf. A199898.
Formula
Empirical: a(n) = (4/3)*n^3 + 6*n^2 + (20/3)*n + 1.
Conjectures from Colin Barker, Feb 23 2018: (Start)
G.f.: x*(3 - x)*(5 - 2*x + x^2) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)
Comments