A199900 Number of -n..n arrays x(0..4) of 5 elements with zero sum, and adjacent elements not both strictly positive and not both strictly negative.

33, 159, 461, 1043, 2031, 3573, 5839, 9021, 13333, 19011, 26313, 35519, 46931, 60873, 77691, 97753, 121449, 149191, 181413, 218571, 261143, 309629, 364551, 426453, 495901, 573483, 659809, 755511, 861243, 977681, 1105523, 1245489, 1398321

Offset

1,1

Comments

Row 5 of A199898.

Links

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

Formula

Empirical: a(n) = (11/12)*n^4 + (49/6)*n^3 + (193/12)*n^2 + (41/6)*n + 1.

Conjectures from Colin Barker, May 16 2018: (Start)

G.f.: x*(33 - 6*x - 4*x^2 - 2*x^3 + x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

Some solutions for n=6:
.-4...-2....0....2....0....2....0....0...-5....2...-1...-2...-4....3...-6...-6
..3....2....3...-4....1...-3...-3....6....5...-1....4....0....6...-6....1....6
.-1...-1...-5....0....0....3....6....0...-3....1...-3....5...-1....2...-1...-1
..6....5....0...-2....5...-3...-3...-6....5...-5....5....0....1...-3....6....4
.-4...-4....2....4...-6....1....0....0...-2....3...-5...-3...-2....4....0...-3

Crossrefs

Cf. A199898.

Sequence in context: A005904 A207078 A182588 * A086504 A233064 A183776

Adjacent sequences: A199897 A199898 A199899 * A199901 A199902 A199903

Keyword

nonn

Author

R. H. Hardin, Nov 11 2011

Status

approved