|
%I #7 Jan 24 2019 11:44:34
%S 16,79,250,613,1276,2371,4054,6505,9928,14551,20626,28429,38260,50443,
%T 65326,83281,104704,130015,159658,194101,233836,279379,331270,390073,
%U 456376,530791,613954,706525,809188,922651,1047646,1184929,1335280
%N Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by more than one.
%H R. H. Hardin, <a href="/A269584/b269584.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = n^4 + 4*n^3 + 5*n^2 + 5*n + 1.
%F Conjectures from _Colin Barker_, Jan 24 2019: (Start)
%F G.f.: x*(16 - x + 15*x^2 - 7*x^3 + x^4) / (1 - x)^5.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F (End)
%e Some solutions for n=6:
%e ..4. .0. .1. .6. .0. .1. .1. .2. .1. .3. .5. .1. .2. .3. .0. .6
%e ..0. .5. .3. .4. .3. .5. .2. .1. .2. .2. .2. .3. .5. .4. .6. .2
%e ..1. .6. .0. .1. .6. .4. .1. .1. .5. .6. .4. .1. .3. .0. .2. .2
%e ..2. .6. .4. .0. .4. .1. .5. .0. .0. .0. .3. .0. .2. .5. .2. .0
%Y Row 4 of A269583.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 01 2016
|
