A268952 - OEIS

%I #9 Jan 17 2019 05:26:15

%S 1,2,4,12,40,153,634,2785,12634,58409,272738,1280233,6024682,28383609,

%T 133772018,630473513,2970963898,13996752665,65924951490,310433985929,

%U 1461486107146,6879181490937,32374728610962,152339562845289

%N Number of length-n 0..4 arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

%H R. H. Hardin, <a href="/A268952/b268952.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 11*a(n-1) -31*a(n-2) -41*a(n-3) +268*a(n-4) -90*a(n-5) -692*a(n-6) +512*a(n-7) +576*a(n-8) -512*a(n-9) for n>11.

%F Empirical g.f.: x*(1 - 9*x + 13*x^2 + 71*x^3 - 154*x^4 - 197*x^5 + 483*x^6 + 210*x^7 - 546*x^8 - 24*x^9 + 192*x^10) / ((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 2*x^2)*(1 - x - 4*x^2)*(1 - 3*x - 8*x^2)). - _Colin Barker_, Jan 17 2019

%e Some solutions for n=8:

%e ..0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0

%e ..1. .0. .1. .1. .1. .1. .1. .1. .1. .1. .1. .1. .0. .1. .1. .1

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

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

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

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

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

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

%Y Column 4 of A268956.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 16 2016