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A267475 Number of length-7 0..n arrays with no following elements larger than the first repeated value. 1

%I

%S 71,1112,8770,44901,171601,532840,1418740,3357537,7240267,14483216,

%T 27233174,48620533,83065269,136640848,217501096,336375073,507134991,

%U 747442216,1079476394,1530752741,2135032537,2933331864,3975033628

%N Number of length-7 0..n arrays with no following elements larger than the first repeated value.

%C Row 7 of A267471.

%H R. H. Hardin, <a href="/A267475/b267475.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^7 + (69/20)*n^6 + (17/2)*n^5 + (97/6)*n^4 + 20*n^3 + (893/60)*n^2 + 6*n + 1.

%F Conjectures from _Colin Barker_, Feb 05 2018: (Start)

%F G.f.: x*(71 + 544*x + 1862*x^2 + 1901*x^3 + 651*x^4 + 4*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=5:

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

%e ..0....0....4....4....3....0....3....4....0....1....0....0....4....3....2....3

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

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

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

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

%e ..4....3....3....1....0....2....2....1....2....3....4....4....3....2....1....0

%Y Cf. A267471.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 15 2016

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Last modified February 2 06:48 EST 2023. Contains 360000 sequences. (Running on oeis4.)