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Number of length-n 0..3 arrays with no adjacent pair x,x+1 repeated.
1

%I #4 Mar 02 2016 11:26:34

%S 4,16,64,253,988,3816,14596,55344,208196,777582,2885120,10640607,

%T 39027196,142415244,517252820,1870499543,6736838192,24172420350,

%U 86428990624,308016010824,1094338584760,3876828265788,13696906252336

%N Number of length-n 0..3 arrays with no adjacent pair x,x+1 repeated.

%C Column 3 of A269656.

%H R. H. Hardin, <a href="/A269651/b269651.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 16*a(n-1) -108*a(n-2) +408*a(n-3) -986*a(n-4) +1704*a(n-5) -2312*a(n-6) +2560*a(n-7) -2355*a(n-8) +1832*a(n-9) -1208*a(n-10) +672*a(n-11) -314*a(n-12) +120*a(n-13) -36*a(n-14) +8*a(n-15) -a(n-16)

%e Some solutions for n=8

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

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

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

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

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

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

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

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

%Y Cf. A269656.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 02 2016