|
%I #9 Feb 06 2018 04:16:47
%S 7,49,315,1981,12327,76237,469623,2884909,17686215,108259885,
%T 661872471,4042575277,24671450343,150466937773,917151735159,
%U 5587651325485,34027698639111,207144227712301,1260572274312087,7668877406965933
%N Number of length-n 0..6 arrays with no following elements greater than or equal to the first repeated value.
%C Column 6 of A267232.
%H R. H. Hardin, <a href="/A267230/b267230.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 27*a(n-1) - 301*a(n-2) + 1785*a(n-3) - 6034*a(n-4) + 11508*a(n-5) - 11304*a(n-6) + 4320*a(n-7) for n > 8.
%F Conjectures from _Colin Barker_, Feb 05 2018: (Start)
%F G.f.: x*(7 - 140*x + 1099*x^2 - 4270*x^3 + 8428*x^4 - 7476*x^5 + 1512*x^6 + 720*x^7) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)^2).
%F a(n) = (-45*2^n - 40*3^n - 45*4^n - 72*5^n + 557*6^n + 5*2^(1 + n)*3^n*n - 72) / 360 for n>1.
%F (End)
%e Some solutions for n=6:
%e 3 2 1 3 1 2 2 0 4 0 2 0 1 3 6 3
%e 6 6 0 6 2 3 3 3 5 2 4 1 5 4 5 6
%e 2 1 3 1 0 5 5 2 2 6 3 0 3 1 5 4
%e 5 3 6 3 4 6 2 5 4 4 1 4 0 4 2 2
%e 2 1 1 4 1 5 0 1 5 0 6 6 3 2 4 0
%e 3 0 6 0 1 2 4 1 2 0 6 6 1 4 0 6
%Y Cf. A267232.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 12 2016
| 