A200886 -id:A200886 - cp's OEIS frontend

A200891 Number of 0..n arrays x(0..7) of 8 elements without any interior element greater than both neighbors.

114, 1691, 11472, 50995, 173606, 491533, 1215616, 2710413, 5567530, 10700151, 19461872, 33793071, 56398174, 90957305, 142375936, 217076281, 323334306, 471666355, 675269520, 950520011, 1317533910, 1800794821, 2429853056

Offset: 1

R. H. Hardin, Nov 23 2011

nonn

Row 6 of A200886.

			Some solutions for n=3
..3....2....2....0....0....3....3....1....1....3....1....3....2....0....0....3
..1....3....0....3....1....0....0....1....3....3....3....3....1....0....0....0
..1....3....3....3....3....0....0....0....3....3....3....1....2....1....3....1
..3....3....3....3....3....3....0....3....0....0....3....0....2....1....3....1
..3....2....3....3....2....3....1....3....1....0....3....0....2....1....0....2
..0....0....0....2....0....1....1....2....3....1....2....1....0....3....2....2
..2....0....1....0....1....0....1....1....3....1....1....1....1....3....2....2
..2....2....1....2....1....0....3....3....2....2....2....3....3....2....2....1

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

Empirical: a(n) = (1/315)*n^8 + (134/315)*n^7 + (21/5)*n^6 + (571/36)*n^5 + (1841/60)*n^4 + (6047/180)*n^3 + (26603/1260)*n^2 + (299/42)*n + 1.
Conjectures from Colin Barker, Oct 16 2017: (Start)
G.f.: x*(114 + 665*x + 357*x^2 - 953*x^3 - 37*x^4 - 47*x^5 + 37*x^6 - 9*x^7 + x^8) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
(End)

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

Original entry on oeis.org

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

Offset: 1

R. H. Hardin, Nov 23 2011

nonn

Row 7 of A200886.

			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

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

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)

cp's OEIS Frontend

A200891 Number of 0..n arrays x(0..7) of 8 elements without any interior element greater than both neighbors.

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