A200892 Number of 0..n arrays x(0..8) of 9 elements without any interior element greater than both neighbors.

200, 4059, 34350, 181336, 710976, 2269938, 6233356, 15250675, 34054592, 70608021, 137674186, 254905378, 451556600, 769941268, 1269757336, 2033423669, 3172578200, 4835901375, 7218440614, 10572623996, 15221164112, 21572066022

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: A219425 A341545 A297318 * A220390 A231803 A185988

Adjacent sequences: A200889 A200890 A200891 * A200893 A200894 A200895

Keyword

nonn

Author

R. H. Hardin, Nov 23 2011

Status

approved