A250143 Number of length 4+2 0..n arrays with the medians of every three consecutive terms nondecreasing.

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

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