|
%I #11 Nov 12 2018 03:01:22
%S 111,2026,16104,81664,311498,974944,2637228,6376143,14100493,28998090,
%T 56144452,103306710,181980592,308701712,506675752,807775485,
%U 1254955947,1905142426,2832649296,4133191084,5928550518,8371971664,11654349620
%N Number of length 6+2 0..n arrays with the medians of every three consecutive terms nondecreasing.
%H R. H. Hardin, <a href="/A250145/b250145.txt">Table of n, a(n) for n = 1..162</a>
%F 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.
%F Conjectures from _Colin Barker_, Nov 11 2018: (Start)
%F 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.
%F 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.
%F (End)
%e Some solutions for n=4:
%e 2 1 2 1 0 4 2 2 0 1 3 1 2 0 2 3
%e 2 4 4 0 0 0 0 0 4 1 1 0 1 0 4 3
%e 2 2 0 2 3 0 0 0 1 3 1 1 2 0 2 4
%e 2 0 2 2 4 4 0 2 0 3 0 3 2 0 0 2
%e 2 2 2 3 3 2 1 3 2 1 1 2 2 2 3 3
%e 2 3 2 1 3 1 3 4 4 3 4 4 3 1 3 4
%e 3 4 2 2 3 4 2 4 2 4 1 4 2 0 4 0
%e 1 3 0 4 3 4 0 3 3 1 3 1 1 4 1 3
%Y Row 6 of A250140.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 13 2014
| 