cp's OEIS Frontend

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

%I A267475 #7 Feb 05 2018 09:36:41
%S A267475 71,1112,8770,44901,171601,532840,1418740,3357537,7240267,14483216,
%T A267475 27233174,48620533,83065269,136640848,217501096,336375073,507134991,
%U A267475 747442216,1079476394,1530752741,2135032537,2933331864,3975033628
%N A267475 Number of length-7 0..n arrays with no following elements larger than the first repeated value.
%C A267475 Row 7 of A267471.
%H A267475 R. H. Hardin, <a href="/A267475/b267475.txt">Table of n, a(n) for n = 1..210</a>
%F A267475 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 A267475 Conjectures from _Colin Barker_, Feb 05 2018: (Start)
%F A267475 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 A267475 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 A267475 (End)
%e A267475 Some solutions for n=5:
%e A267475 ..3....4....0....4....5....2....5....3....2....0....5....5....1....5....0....2
%e A267475 ..0....0....4....4....3....0....3....4....0....1....0....0....4....3....2....3
%e A267475 ..1....1....1....0....4....4....0....1....5....5....4....2....3....5....0....2
%e A267475 ..3....4....2....0....4....2....4....0....5....0....4....4....0....4....3....1
%e A267475 ..4....5....3....4....1....0....1....1....4....2....2....0....5....1....5....2
%e A267475 ..3....0....3....1....0....4....4....5....2....3....3....1....4....4....2....4
%e A267475 ..4....3....3....1....0....2....2....1....2....3....4....4....3....2....1....0
%Y A267475 Cf. A267471.
%K A267475 nonn
%O A267475 1,1
%A A267475 _R. H. Hardin_, Jan 15 2016