A250141 Number of length 2+2 0..n arrays with the medians of every three consecutive terms nondecreasing.

14, 67, 204, 485, 986, 1799, 3032, 4809, 7270, 10571, 14884, 20397, 27314, 35855, 46256, 58769, 73662, 91219, 111740, 135541, 162954, 194327, 230024, 270425, 315926, 366939, 423892, 487229, 557410, 634911, 720224, 813857, 916334, 1028195

Offset

1,1

Links

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

Formula

Empirical: a(n) = (2/3)*n^4 + (10/3)*n^3 + (16/3)*n^2 + (11/3)*n + 1.

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

G.f.: x*(14 - 3*x + 9*x^2 - 5*x^3 + x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

Some solutions for n=6:
  3  6  0  3  0  4  1  4  1  4  3  6  6  4  0  2
  1  4  3  3  1  0  4  5  4  6  3  0  6  1  2  6
  4  4  5  4  5  3  2  4  3  2  5  5  6  4  2  2
  5  0  5  5  6  3  4  5  4  5  4  5  4  5  4  3

Crossrefs

Row 2 of A250140.

Sequence in context: A280401 A221703 A064096 * A071616 A008529 A075480

Adjacent sequences: A250138 A250139 A250140 * A250142 A250143 A250144

Keyword

nonn

Author

R. H. Hardin, Nov 13 2014

Status

approved