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A200890 Number of 0..n arrays x(0..6) of 7 elements without any interior element greater than both neighbors. 1
65, 704, 3823, 14288, 42182, 105813, 235538, 478467, 904111, 1611038, 2734601, 4455802, 7011356, 10705019, 15920244, 23134229, 32933421, 46030540, 63283187, 85714100, 114533122, 151160945, 197254694, 254735415, 325817531, 413040330 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 5 of A200886.

LINKS

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

FORMULA

Empirical: a(n) = (4/315)*n^7 + (7/9)*n^6 + (241/45)*n^5 + (1067/72)*n^4 + (3757/180)*n^3 + (1145/72)*n^2 + (2629/420)*n + 1.

Conjectures from Colin Barker, Oct 16 2017: (Start)

G.f.: x*(65 + 184*x + 11*x^2 - 224*x^3 + 48*x^4 - 27*x^5 + 8*x^6 - x^7) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

EXAMPLE

Some solutions for n=3

..0....2....3....2....2....3....2....0....2....0....2....2....3....2....1....1

..1....3....0....2....0....2....2....3....3....3....0....0....1....2....0....2

..1....3....0....3....3....2....1....3....3....3....3....1....2....3....2....2

..0....0....2....3....3....0....2....3....3....2....3....1....2....3....2....2

..2....1....3....0....2....0....2....2....0....3....2....0....2....3....2....2

..2....1....3....0....2....2....0....0....1....3....0....1....1....3....0....0

..2....3....2....2....1....3....1....0....3....3....1....1....0....3....1....1

CROSSREFS

Sequence in context: A297317 A224099 A220229 * A268265 A353939 A351269

Adjacent sequences:  A200887 A200888 A200889 * A200891 A200892 A200893

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 23 2011

STATUS

approved

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Last modified May 22 16:57 EDT 2022. Contains 353957 sequences. (Running on oeis4.)