A269644 - OEIS

%I #8 Jan 25 2019 11:44:42

%S 20,969,9928,55225,216528,675151,1789528,4200933,8974480,17780443,

%T 33120936,58606993,99291088,162060135,256094008,393394621,589390608,

%U 863622643,1240514440,1750234473,2429653456,3323402623,4485037848

%N Number of length-7 0..n arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

%H R. H. Hardin, <a href="/A269644/b269644.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^7 + 7*n^6 + 6*n^5 + 20*n^4 - 22*n^3 + 28*n^2 - 37*n + 13 for n>2.

%F Conjectures from _Colin Barker_, Jan 25 2019: (Start)

%F G.f.: x*(20 + 809*x + 2736*x^2 + 1813*x^3 - 152*x^4 - 31*x^5 - 240*x^6 + 123*x^7 - 44*x^8 + 6*x^9)  / (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>10.

%F (End)

%e Some solutions for n=3:

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

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

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

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

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

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

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

%Y Row 7 of A269640.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 02 2016