A269692 - OEIS

%I #8 Jan 28 2019 09:51:49

%S 40,525,3544,14465,44556,114205,256880,523809,989380,1757261,2967240,

%T 4802785,7499324,11353245,16731616,24082625,33946740,46968589,

%U 63909560,85661121,113258860,147897245,190945104,243961825,308714276,387194445

%N Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by plus or minus one modulo n+1.

%H R. H. Hardin, <a href="/A269692/b269692.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^6 + 6*n^5 + 15*n^4 + 8*n^3 - 7*n^2 - 4*n + 1 for n>1.

%F Conjectures from _Colin Barker_, Jan 28 2019: (Start)

%F G.f.: x*(40 + 245*x + 709*x^2 - 718*x^3 + 750*x^4 - 427*x^5 + 141*x^6 - 20*x^7) / (1 - x)^7.

%F 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>8.

%F (End)

%e Some solutions for n=3:

%e ..3. .3. .1. .0. .2. .1. .2. .1. .1. .1. .2. .1. .3. .3. .2. .1

%e ..2. .2. .0. .1. .0. .3. .1. .2. .1. .2. .3. .1. .3. .0. .0. .1

%e ..2. .2. .1. .3. .1. .0. .1. .1. .1. .1. .2. .0. .1. .1. .3. .0

%e ..0. .0. .0. .3. .3. .1. .1. .0. .2. .2. .1. .3. .1. .3. .1. .2

%e ..3. .2. .3. .1. .1. .1. .0. .0. .3. .0. .2. .1. .0. .3. .1. .1

%e ..1. .2. .1. .2. .1. .2. .3. .0. .3. .0. .2. .2. .3. .3. .2. .0

%Y Row 6 of A269690.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 03 2016