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A200892 Number of 0..n arrays x(0..8) of 9 elements without any interior element greater than both neighbors. 1
200, 4059, 34350, 181336, 710976, 2269938, 6233356, 15250675, 34054592, 70608021, 137674186, 254905378, 451556600, 769941268, 1269757336, 2033423669, 3172578200, 4835901375, 7218440614, 10572623996, 15221164112, 21572066022 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 7 of A200886.

LINKS

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

FORMULA

Empirical: a(n) = (2/2835)*n^9 + (131/630)*n^8 + (2803/945)*n^7 + (1349/90)*n^6 + (41449/1080)*n^5 + (20423/360)*n^4 + (1149293/22680)*n^3 + (22741/840)*n^2 + (2011/252)*n + 1.

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

G.f.: x*(200 + 2059*x + 2760*x^2 - 3509*x^3 - 1714*x^4 + 288*x^5 + 208*x^6 - 45*x^7 + 10*x^8 - x^9) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

(End)

EXAMPLE

Some solutions for n=3

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

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

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

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

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

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

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

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

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

CROSSREFS

Sequence in context: A218846 A219425 A297318 * A220390 A231803 A185988

Adjacent sequences:  A200889 A200890 A200891 * A200893 A200894 A200895

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 23 2011

STATUS

approved

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Last modified February 18 21:20 EST 2020. Contains 332028 sequences. (Running on oeis4.)