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A250143 Number of length 4+2 0..n arrays with the medians of every three consecutive terms nondecreasing. 1
41, 391, 1959, 6902, 19446, 46914, 100962, 199023, 365959, 635921, 1054417, 1680588, 2589692, 3875796, 5654676, 8066925, 11281269, 15498091, 20953163, 27921586, 36721938, 47720630, 61336470, 78045435, 98385651, 122962581 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

FORMULA

Empirical: a(n) = (13/45)*n^6 + (5/2)*n^5 + (595/72)*n^4 + (53/4)*n^3 + (3941/360)*n^2 + (19/4)*n + 1.

Conjectures from Colin Barker, Nov 11 2018: (Start)

G.f.: x*(41 + 104*x + 83*x^2 - 35*x^3 + 21*x^4 - 7*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

EXAMPLE

Some solutions for n=6:

  6  0  5  2  0  0  0  0  0  2  0  4  1  1  4  3

  0  0  2  5  3  4  6  2  0  3  5  6  3  1  0  3

  1  4  2  2  0  0  2  3  1  5  4  0  2  6  4  1

  6  0  2  1  4  5  2  6  0  5  4  6  2  5  6  3

  6  3  6  3  5  5  6  1  6  5  5  6  3  2  6  4

  5  6  6  5  4  6  2  5  6  3  1  4  1  6  2  5

CROSSREFS

Row 4 of A250140.

Sequence in context: A196576 A090211 A274725 * A069594 A124338 A008356

Adjacent sequences:  A250140 A250141 A250142 * A250144 A250145 A250146

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 13 2014

STATUS

approved

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Last modified December 4 19:40 EST 2021. Contains 349526 sequences. (Running on oeis4.)