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A199899
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Number of -n..n arrays x(0..3) of 4 elements with zero sum, and adjacent elements not both strictly positive and not both strictly negative.
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3
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15, 49, 111, 209, 351, 545, 799, 1121, 1519, 2001, 2575, 3249, 4031, 4929, 5951, 7105, 8399, 9841, 11439, 13201, 15135, 17249, 19551, 22049, 24751, 27665, 30799, 34161, 37759, 41601, 45695, 50049, 54671, 59569, 64751, 70225, 75999, 82081, 88479, 95201
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OFFSET
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1,1
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COMMENTS
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Row 4 of A199898.
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..200
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FORMULA
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Empirical: a(n) = (4/3)*n^3 + 6*n^2 + (20/3)*n + 1.
Conjectures from Colin Barker, Feb 23 2018: (Start)
G.f.: x*(3 - x)*(5 - 2*x + x^2) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)
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EXAMPLE
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Some solutions for n=6:
..3....3....4...-2....5...-2....5...-3....4...-3....0....2....0....6....3....1
..0...-6...-4....6...-4....1...-5....2...-5....6....2...-2....5...-1...-5...-5
..2....3....1...-6....3...-4....3...-1....5....0....0....5...-5....0....6....0
.-5....0...-1....2...-4....5...-3....2...-4...-3...-2...-5....0...-5...-4....4
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CROSSREFS
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Cf. A199898.
Sequence in context: A228219 A272039 A241577 * A020257 A298511 A349855
Adjacent sequences: A199896 A199897 A199898 * A199900 A199901 A199902
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Nov 11 2011
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STATUS
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approved
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