A250145 Number of length 6+2 0..n arrays with the medians of every three consecutive terms nondecreasing.

111, 2026, 16104, 81664, 311498, 974944, 2637228, 6376143, 14100493, 28998090, 56144452, 103306710, 181980592, 308701712, 506675752, 807775485, 1254955947, 1905142426, 2832649296, 4133191084, 5928550518, 8371971664, 11654349620

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..162

Formula

Empirical: a(n) = (1/12)*n^8 + (1487/1260)*n^7 + (4757/720)*n^6 + (13757/720)*n^5 + (4519/144)*n^4 + (21611/720)*n^3 + (2957/180)*n^2 + (2183/420)*n + 1.

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

G.f.: x*(111 + 1027*x + 1866*x^2 + 340*x^3 + 68*x^4 - 80*x^5 + 36*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>10.

(End)

Example

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

Crossrefs

Row 6 of A250140.

Sequence in context: A303256 A137465 A101152 * A075859 A264466 A302384

Adjacent sequences: A250142 A250143 A250144 * A250146 A250147 A250148

Keyword

nonn

Author

R. H. Hardin, Nov 13 2014

Status

approved