cp's OEIS Frontend

A243636 Number of length n+2 0..5 arrays with no three unequal elements in a row and new values 0..5 introduced in 0..5 order.

%I A243636 #8 Nov 02 2018 12:28:03
%S A243636 4,9,21,51,127,324,844,2243,6073,16736,46892,133443,385277,1127352,
%T A243636 3339464,10003395,30269129,92422160,284470820,881804563,2750412037,
%U A243636 8625112792,27174303856,85960269683,272856760081,868664396112
%N A243636 Number of length n+2 0..5 arrays with no three unequal elements in a row and new values 0..5 introduced in 0..5 order.
%H A243636 R. H. Hardin, <a href="/A243636/b243636.txt">Table of n, a(n) for n = 1..210</a>
%F A243636 Empirical: a(n) = 9*a(n-1) - 25*a(n-2) + 7*a(n-3) + 64*a(n-4) - 54*a(n-5) - 48*a(n-6) + 32*a(n-7) + 16*a(n-8).
%F A243636 Empirical g.f.: x*(4 - 27*x + 40*x^2 + 59*x^3 - 126*x^4 - 51*x^5 + 80*x^6 + 32*x^7) / ((1 - x)*(1 - 2*x)*(1 - 2*x - x^2)*(1 - 2*x - 2*x^2)*(1 - 2*x - 4*x^2)). - _Colin Barker_, Nov 02 2018
%e A243636 Some solutions for n=6:
%e A243636 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A243636 ..1....0....1....0....1....1....1....1....0....0....1....0....0....0....0....1
%e A243636 ..1....0....1....0....1....0....0....1....1....1....1....0....0....1....1....1
%e A243636 ..1....0....2....1....1....1....0....2....1....0....1....1....1....1....0....0
%e A243636 ..0....0....2....1....2....1....1....1....2....0....1....1....1....2....1....1
%e A243636 ..1....0....0....1....2....0....1....2....2....2....1....2....0....2....1....0
%e A243636 ..1....1....0....1....2....1....0....2....2....2....0....2....0....3....0....0
%e A243636 ..1....1....1....1....3....1....1....2....3....0....1....1....0....2....1....2
%Y A243636 Column 5 of A243641.
%K A243636 nonn
%O A243636 1,1
%A A243636 _R. H. Hardin_, Jun 08 2014