|
%I #7 Feb 05 2018 17:10:08
%S 6,47,176,470,1030,1981,3472,5676,8790,13035,18656,25922,35126,46585,
%T 60640,77656,98022,122151,150480,183470,221606,265397,315376,372100,
%U 436150,508131,588672,678426,778070,888305,1009856,1143472,1289926
%N Number of length-4 0..n arrays with no following elements greater than or equal to the first repeated value.
%C Row 4 of A267232.
%H R. H. Hardin, <a href="/A267233/b267233.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = n^4 + (17/6)*n^3 + 2*n^2 + (1/6)*n.
%F Conjectures from _Colin Barker_, Feb 05 2018: (Start)
%F G.f.: x*(6 + 17*x + x^2) / (1 - x)^5.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F (End)
%e Some solutions for n=6:
%e ..4....5....2....2....0....4....4....5....0....4....3....2....0....4....0....3
%e ..3....3....4....0....5....2....0....6....3....5....4....4....3....3....2....6
%e ..1....3....2....5....5....3....1....2....5....5....2....1....0....2....4....4
%e ..4....0....6....4....4....1....4....1....4....3....3....3....6....4....2....6
%Y Cf. A267232.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 12 2016
| 