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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 2 of A200871.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

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: A247792 A096000 A047672 * A212755 A048480 A116970

Adjacent sequences:  A200869 A200870 A200871 * A200873 A200874 A200875

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 23 2011

STATUS

approved

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Last modified October 14 23:57 EDT 2019. Contains 328025 sequences. (Running on oeis4.)