A199901 Number of -n..n arrays x(0..5) of 6 elements with zero sum, and adjacent elements not both strictly positive and not both strictly negative.

75, 533, 2035, 5725, 13363, 27457, 51395, 89577, 147547, 232125, 351539, 515557, 735619, 1024969, 1398787, 1874321, 2471019, 3210661, 4117491, 5218349, 6542803, 8123281, 9995203, 12197113, 14770811, 17761485, 21217843, 25192245, 29740835

Offset

1,1

Comments

Row 6 of A199898.

Links

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

Formula

Empirical: a(n) = (11/10)*n^5 + (55/6)*n^4 + (55/2)*n^3 + (173/6)*n^2 + (37/5)*n + 1.

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

G.f.: x*(75 + 83*x - 38*x^2 + 10*x^3 + 3*x^4 - x^5) / (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)

Example

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

Crossrefs

Cf. A199898.

Sequence in context: A015223 A129625 A133382 * A251249 A264673 A320618

Adjacent sequences: A199898 A199899 A199900 * A199902 A199903 A199904

Keyword

nonn

Author

R. H. Hardin, Nov 11 2011

Status

approved