A269540 - OEIS

%I #7 Jan 24 2019 09:13:59

%S 22,418,2878,12214,38878,102202,234358,485038,926854,1661458,2826382,

%T 4602598,7222798,10980394,16239238,23444062,33131638,45942658,

%U 62634334,84093718,111351742,145597978,188196118,240700174,304871398,382695922

%N Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by other than one.

%H R. H. Hardin, <a href="/A269540/b269540.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^6 + 6*n^5 + 5*n^4 + 12*n^3 - 6*n^2 + 6*n - 2.

%F Conjectures from _Colin Barker_, Jan 24 2019: (Start)

%F G.f.: 2*x*(11 + 132*x + 207*x^2 + 38*x^3 - 21*x^4 - 6*x^5 - x^6) / (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>7.

%F (End)

%e Some solutions for n=3:

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

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

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

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

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

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

%Y Row 6 of A269537.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 29 2016