A269693 - OEIS

%I #8 Jan 28 2019 09:53:57

%S 66,1347,13168,69405,260616,786079,2031072,4674393,9831160,19235931,

%T 35471184,62246197,104731368,169953015,267253696,408823089,610304472,

%U 891481843,1277052720,1797491661,2490009544,3399613647,4580273568

%N Number of length-7 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="/A269693/b269693.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^7 + 7*n^6 + 21*n^5 + 15*n^4 - 13*n^3 - 11*n^2 + 3*n + 1 for n>1.

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

%F G.f.: x*(66 + 819*x + 4240*x^2 - 1919*x^3 + 3268*x^4 - 2323*x^5 + 1184*x^6 - 337*x^7 + 42*x^8) / (1 - x)^8.

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>9.

%F (End)

%e Some solutions for n=3:

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

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

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

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

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

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

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

%Y Row 7 of A269690.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 03 2016