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A200872
Number of 0..n arrays x(0..3) of 4 elements without any interior element greater than both neighbors or less than both neighbors.
1
10, 37, 94, 195, 356, 595, 932, 1389, 1990, 2761, 3730, 4927, 6384, 8135, 10216, 12665, 15522, 18829, 22630, 26971, 31900, 37467, 43724, 50725, 58526, 67185, 76762, 87319, 98920, 111631, 125520, 140657, 157114, 174965, 194286, 215155, 237652, 261859
OFFSET
1,1
COMMENTS
Row 2 of A200871.
LINKS
FORMULA
Empirical: a(n) = (1/12)*n^4 + (3/2)*n^3 + (47/12)*n^2 + (7/2)*n + 1.
Conjectures from Colin Barker, Oct 16 2017: (Start)
G.f.: x*(10 - 13*x + 9*x^2 - 5*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=3
..1....0....2....0....3....0....2....2....1....0....0....0....3....0....3....0
..2....2....3....1....3....0....2....2....3....2....0....0....2....2....1....1
..2....3....3....1....2....1....1....2....3....2....0....1....2....2....1....3
..1....3....0....0....1....1....0....2....1....1....0....2....2....0....1....3
CROSSREFS
Sequence in context: A372373 A096000 A047672 * A212755 A048480 A116970
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 23 2011
STATUS
approved