cp's OEIS Frontend

A268941 Number of length-n 0..5 arrays with no repeated value unequal to the previous repeated value plus one mod 5+1.

%I A268941 #8 Jan 17 2019 02:55:43
%S A268941 6,36,210,1206,6834,38322,213042,1175850,6450402,35200458,191222994,
%T A268941 1034688474,5579060610,29989217034,160755450546,859578198138,
%U A268941 4585950964578,24416800390890,129760544069778,688431162218202
%N A268941 Number of length-n 0..5 arrays with no repeated value unequal to the previous repeated value plus one mod 5+1.
%H A268941 R. H. Hardin, <a href="/A268941/b268941.txt">Table of n, a(n) for n = 1..210</a>
%F A268941 Empirical: a(n) = 9*a(n-1) - 14*a(n-2) - 30*a(n-3).
%F A268941 Conjectures from _Colin Barker_, Jan 17 2019: (Start)
%F A268941 G.f.: 6*x*(1 - 3*x - 5*x^2) / ((1 - 5*x)*(1 - 4*x - 6*x^2)).
%F A268941 a(n) = (-12*5^(1+n) + (35-11*sqrt(10))*(2-sqrt(10))^n + (2+sqrt(10))^n*(35+11*sqrt(10))) / 10.
%F A268941 (End)
%e A268941 Some solutions for n=6:
%e A268941 ..5. .2. .0. .3. .0. .2. .4. .4. .1. .2. .4. .2. .1. .0. .4. .5
%e A268941 ..2. .5. .4. .4. .2. .0. .2. .1. .4. .3. .3. .5. .4. .2. .3. .3
%e A268941 ..5. .0. .5. .3. .2. .1. .4. .2. .2. .2. .3. .3. .0. .4. .0. .4
%e A268941 ..0. .1. .1. .3. .3. .4. .1. .4. .3. .3. .2. .2. .3. .3. .2. .5
%e A268941 ..4. .4. .3. .1. .0. .4. .4. .3. .3. .1. .4. .5. .4. .0. .0. .0
%e A268941 ..1. .2. .3. .4. .1. .0. .4. .5. .5. .5. .4. .1. .3. .1. .2. .3
%Y A268941 Column 5 of A268944.
%K A268941 nonn
%O A268941 1,1
%A A268941 _R. H. Hardin_, Feb 16 2016