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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.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 11 2011
STATUS
approved