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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 5 12:47 EST 2023. Contains 360084 sequences. (Running on oeis4.)