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%I #15 Mar 17 2018 05:45:47
%S 88,1071,6130,23627,71278,181885,410828,845517,1617004,2913955,
%T 4999182,8228935,13075154,20150881,30239032,44324729,63631392,
%U 89660791,124237258,169556259,228237526,303382949,398639428,518266885,667211636,851185323
%N Number of arrays of the median of three adjacent elements of some length 9 0..n array.
%C Row 7 of A228740.
%H R. H. Hardin, <a href="/A228744/b228744.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (5/126)*n^7 + (4/3)*n^6 + (829/90)*n^5 + (93/4)*n^4 + (509/18)*n^3 + (221/12)*n^2 + (453/70)*n + 1.
%F Conjectures from _Colin Barker_, Mar 16 2018: (Start)
%F G.f.: x*(88 + 367*x + 26*x^2 - 353*x^3 + 86*x^4 - 21*x^5 + 8*x^6 - x^7) / (1 - x)^8.
%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
%F (End)
%e Some solutions for n=4:
%e 2 4 0 4 3 2 0 4 1 2 3 1 4 2 1 1
%e 3 1 1 3 0 3 1 2 1 2 2 2 4 2 1 2
%e 2 4 4 2 1 0 1 4 4 3 2 4 0 3 0 3
%e 2 0 2 1 0 0 0 4 3 3 0 4 4 4 4 3
%e 2 2 4 2 0 0 0 4 4 4 2 3 2 4 4 4
%e 0 1 4 2 0 2 1 4 3 4 0 2 4 0 4 2
%e 1 1 4 2 2 4 4 1 0 2 1 2 2 0 4 4
%Y Cf. A228740.
%K nonn
%O 1,1
%A _R. H. Hardin_, Sep 01 2013
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