A269492 - OEIS

%I #8 Jan 23 2019 10:07:34

%S 7,49,343,2389,16579,114695,791381,5448185,37435583,256804141,

%T 1759152499,12035747757,82258781115,561684075373,3832259642203,

%U 26128574285113,178038236615119,1212498463318805,8253697161562331,56161736795827953

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

%H R. H. Hardin, <a href="/A269492/b269492.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 30*a(n-1) - 353*a(n-2) + 1992*a(n-3) - 4976*a(n-4) + 1872*a(n-5) + 8202*a(n-6) + 1800*a(n-7) - 210*a(n-8) - 36*a(n-9).

%F Empirical g.f.: x*(7 - 161*x + 1344*x^2 - 4548*x^3 + 3212*x^4 + 8106*x^5 + 1656*x^6 - 208*x^7 - 34*x^8) / ((1 - 6*x)*(1 - 24*x + 209*x^2 - 738*x^3 + 548*x^4 + 1416*x^5 + 294*x^6 - 36*x^7 - 6*x^8)). - _Colin Barker_, Jan 23 2019

%e Some solutions for n=6:

%e ..1. .0. .0. .5. .0. .0. .2. .0. .5. .3. .0. .6. .6. .5. .6. .4

%e ..6. .0. .2. .3. .1. .0. .4. .0. .4. .0. .3. .0. .2. .0. .4. .2

%e ..6. .3. .1. .4. .4. .4. .5. .3. .2. .1. .2. .0. .4. .6. .1. .0

%e ..0. .3. .4. .6. .1. .3. .6. .5. .6. .6. .5. .0. .0. .2. .4. .2

%e ..6. .1. .5. .4. .5. .2. .1. .5. .6. .3. .5. .1. .5. .0. .6. .4

%e ..2. .6. .0. .2. .3. .3. .0. .1. .0. .6. .3. .3. .2. .0. .4. .1

%Y Column 6 of A269494.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 28 2016