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 A250376 Number of length 3+6 0..n arrays with every seven consecutive terms having the maximum of some three terms equal to the minimum of the remaining four terms. 1

%I #7 Nov 13 2018 12:48:48

%S 252,7168,69984,396745,1616636,5272892,14647808,36038649,80620540,

%T 167049696,324977632,599664273,1057895164,1795425260,2946189056,

%U 4693534097,7283752188,11042199904,16392317280,23877870841,34188764412

%N Number of length 3+6 0..n arrays with every seven consecutive terms having the maximum of some three terms equal to the minimum of the remaining four terms.

%H R. H. Hardin, <a href="/A250376/b250376.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (3/7)*n^8 + (57/7)*n^7 + (141/4)*n^6 + (202/3)*n^5 + (147/2)*n^4 + 44*n^3 + (443/28)*n^2 + (137/21)*n + 1.

%F Conjectures from _Colin Barker_, Nov 13 2018: (Start)

%F G.f.: x*(252 + 4900*x + 14544*x^2 + 3769*x^3 - 5005*x^4 - 1252*x^5 + 80*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>9.

%F (End)

%e Some solutions for n=3:

%e ..0....2....1....3....1....1....0....3....3....0....3....1....0....0....0....3

%e ..2....2....1....2....3....1....1....2....1....3....2....1....1....0....0....3

%e ..1....3....1....0....2....0....1....1....3....2....2....0....1....3....0....1

%e ..2....2....0....3....1....1....0....0....2....3....0....2....3....0....0....1

%e ..2....3....0....2....2....3....1....3....1....2....1....1....3....0....0....0

%e ..1....1....0....2....0....3....2....0....2....2....2....2....1....0....1....1

%e ..0....1....0....2....0....2....2....1....3....3....3....2....0....0....2....2

%e ..1....3....2....2....1....0....1....2....3....1....2....1....0....3....1....3

%e ..2....2....0....3....3....1....1....2....1....1....3....1....2....2....0....3

%Y Row 3 of A250373.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 19 2014

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Last modified September 26 02:15 EDT 2023. Contains 365649 sequences. (Running on oeis4.)