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%I #8 Jan 22 2019 06:25:35
%S 92,1722,13868,69235,255576,767172,1981512,4566213,9621220,18861326,
%T 34844052,61247927,103206208,167701080,264023376,404302857,604114092,
%U 883162978,1266058940,1783177851,2471620712,3376273132,4550970648
%N Number of length-7 0..n arrays with no repeated value greater than the previous repeated value.
%H R. H. Hardin, <a href="/A269439/b269439.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = n^7 + 7*n^6 + 16*n^5 + (71/3)*n^4 + (139/6)*n^3 + (43/3)*n^2 + (35/6)*n + 1.
%F Conjectures from _Colin Barker_, Jan 22 2019: (Start)
%F G.f.: x*(92 + 986*x + 2668*x^2 + 1355*x^3 + 8*x^4 - 76*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. .3. .0. .2. .1. .4. .0. .3. .4. .0. .1. .2. .0. .4. .3. .4
%e ..2. .2. .1. .0. .2. .4. .1. .1. .3. .3. .4. .1. .4. .0. .0. .1
%e ..0. .4. .0. .2. .1. .3. .2. .0. .4. .2. .3. .3. .2. .1. .2. .2
%e ..0. .1. .4. .3. .2. .4. .3. .4. .2. .3. .0. .1. .0. .4. .4. .3
%e ..4. .1. .4. .3. .4. .2. .3. .0. .2. .1. .2. .0. .3. .1. .1. .0
%e ..2. .0. .1. .2. .3. .1. .2. .0. .3. .3. .0. .1. .3. .4. .2. .3
%e ..3. .1. .4. .4. .2. .4. .0. .3. .2. .0. .3. .3. .1. .1. .3. .4
%Y Row 7 of A269435.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 26 2016