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 A250143 Number of length 4+2 0..n arrays with the medians of every three consecutive terms nondecreasing. 1

%I #11 Nov 12 2018 03:00:59

%S 41,391,1959,6902,19446,46914,100962,199023,365959,635921,1054417,

%T 1680588,2589692,3875796,5654676,8066925,11281269,15498091,20953163,

%U 27921586,36721938,47720630,61336470,78045435,98385651,122962581

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

%H R. H. Hardin, <a href="/A250143/b250143.txt">Table of n, a(n) for n = 1..210</a>

%F 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.

%F Conjectures from _Colin Barker_, Nov 11 2018: (Start)

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

%F 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.

%F (End)

%e Some solutions for n=6:

%e 6 0 5 2 0 0 0 0 0 2 0 4 1 1 4 3

%e 0 0 2 5 3 4 6 2 0 3 5 6 3 1 0 3

%e 1 4 2 2 0 0 2 3 1 5 4 0 2 6 4 1

%e 6 0 2 1 4 5 2 6 0 5 4 6 2 5 6 3

%e 6 3 6 3 5 5 6 1 6 5 5 6 3 2 6 4

%e 5 6 6 5 4 6 2 5 6 3 1 4 1 6 2 5

%Y Row 4 of A250140.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 13 2014

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Last modified October 4 13:35 EDT 2023. Contains 365885 sequences. (Running on oeis4.)