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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 28 15:37 EST 2023. Contains 359895 sequences. (Running on oeis4.)