cp's OEIS Frontend

A269778 Number of length-6 0..n arrays with every repeated value unequal to the previous repeated value plus one mod n+1.

%I A269778 #8 Jan 29 2019 09:27:03
%S A269778 40,624,3816,15040,45600,115920,259504,527616,994680,1764400,2976600,
%T A269778 4814784,7514416,11371920,16754400,24110080,33979464,47007216,
%U A269778 63954760,85713600,113319360,147966544,191024016,244051200,308815000,387307440
%N A269778 Number of length-6 0..n arrays with every repeated value unequal to the previous repeated value plus one mod n+1.
%H A269778 R. H. Hardin, <a href="/A269778/b269778.txt">Table of n, a(n) for n = 1..210</a>
%F A269778 Empirical: a(n) = n^6 + 6*n^5 + 15*n^4 + 14*n^3 + 4*n^2.
%F A269778 Conjectures from _Colin Barker_, Jan 29 2019: (Start)
%F A269778 G.f.: 8*x*(5 + 43*x + 36*x^2 + 4*x^3 + 2*x^4) / (1 - x)^7.
%F A269778 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A269778 (End)
%e A269778 Some solutions for n=3:
%e A269778 ..3. .1. .3. .1. .1. .3. .3. .1. .2. .2. .3. .3. .0. .2. .1. .2
%e A269778 ..3. .0. .0. .3. .3. .3. .2. .2. .3. .2. .3. .0. .3. .0. .0. .3
%e A269778 ..1. .3. .0. .3. .3. .3. .0. .3. .2. .1. .3. .3. .3. .0. .0. .1
%e A269778 ..1. .2. .1. .0. .3. .3. .2. .3. .1. .1. .2. .0. .0. .0. .3. .0
%e A269778 ..2. .1. .2. .2. .3. .0. .1. .0. .2. .2. .3. .1. .2. .0. .0. .3
%e A269778 ..3. .2. .2. .2. .0. .1. .2. .3. .0. .1. .1. .1. .3. .3. .1. .0
%Y A269778 Row 6 of A269776.
%K A269778 nonn
%O A269778 1,1
%A A269778 _R. H. Hardin_, Mar 04 2016