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

1,1

Comments

Row 4 of A199898.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

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)

Example

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

Crossrefs

Cf. A199898.

Sequence in context: A228219 A272039 A241577 * A020257 A298511 A349855

Adjacent sequences: A199896 A199897 A199898 * A199900 A199901 A199902

Keyword

nonn

Author

R. H. Hardin, Nov 11 2011

Status

approved