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A250144
Number of length 5+2 0..n arrays with the medians of every three consecutive terms nondecreasing.
1
68, 900, 5696, 24125, 79200, 217856, 526032, 1149057, 2318140, 4383764, 7856784, 13458029, 22177208, 35341920, 54697568, 82498977, 121614516, 175643524, 249047840, 347298237, 477036560, 646254368, 864488880, 1143037025, 1495188396
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = (10/63)*n^7 + (163/90)*n^6 + (1421/180)*n^5 + (625/36)*n^4 + (751/36)*n^3 + (2489/180)*n^2 + (178/35)*n + 1.
Conjectures from Colin Barker, Nov 11 2018: (Start)
G.f.: x*(68 + 356*x + 400*x^2 - 51*x^3 + 48*x^4 - 28*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=5:
1 0 3 2 1 2 1 4 2 1 3 1 1 1 0 0
0 2 0 4 0 1 3 2 1 1 0 1 0 3 2 0
0 0 1 0 0 3 5 3 0 5 1 4 1 1 2 0
1 0 1 3 5 4 1 4 1 3 1 4 2 4 2 5
1 0 5 4 1 5 3 4 2 2 1 1 0 3 5 2
5 0 2 2 2 0 4 4 4 4 0 5 1 3 1 1
1 0 3 4 4 4 0 1 4 5 4 4 4 5 3 3
CROSSREFS
Row 5 of A250140.
Sequence in context: A166398 A200876 A039507 * A250338 A223374 A360656
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 13 2014
STATUS
approved