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A199902 Number of -n..n arrays x(0..6) of 7 elements with zero sum, and adjacent elements not both strictly positive and not both strictly negative. 1
171, 1783, 8823, 30199, 82555, 193689, 406575, 783989, 1413739, 2414499, 3942247, 6197307, 9431995, 13958869, 20159583, 28494345, 39511979, 53860591, 72298839, 95707807, 125103483, 161649841, 206672527, 261673149, 328344171, 408584411 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 7 of A199898.

LINKS

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

FORMULA

Empirical: a(n) = (151/180)*n^6 + (163/15)*n^5 + (377/9)*n^4 + (395/6)*n^3 + (7429/180)*n^2 + (93/10)*n + 1.

Conjectures from Colin Barker, May 17 2018: (Start)

G.f.: x*(171 + 586*x - 67*x^2 - 104*x^3 + 25*x^4 - 8*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

EXAMPLE

Some solutions for n=6:

.-3....0....1....1....3....1....0....3....0....0...-5...-3....0....3....0....4

..4....4...-2....0...-1...-5....0...-4....0....2....3....5...-6....0...-6....0

.-2...-2....3...-3....3....1...-5....3...-1....0....0....0....1...-5....4...-3

..5....1....0....5...-6...-3....5...-5....1...-5....6...-6...-6....2...-5....2

.-3...-1...-5...-6....4....5...-1....4....0....4...-3....0....6...-1....3...-5

..5....1....5....4...-5...-3....5...-2...-4....0....2....6...-1....5...-2....5

.-6...-3...-2...-1....2....4...-4....1....4...-1...-3...-2....6...-4....6...-3

CROSSREFS

Cf. A199898.

Sequence in context: A036518 A187133 A185838 * A251223 A186868 A185611

Adjacent sequences:  A199899 A199900 A199901 * A199903 A199904 A199905

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 11 2011

STATUS

approved

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Last modified November 20 10:09 EST 2019. Contains 329334 sequences. (Running on oeis4.)