A269411 - OEIS

%I #7 Jan 21 2019 10:06:44

%S 12,159,804,2670,6960,15477,30744,56124,95940,155595,241692,362154,

%T 526344,745185,1031280,1399032,1864764,2446839,3165780,4044390,

%U 5107872,6383949,7902984,9698100,11805300,14263587,17115084,20405154,24182520

%N Number of length-5 0..n arrays with no repeated value greater than or equal to the previous repeated value.

%H R. H. Hardin, <a href="/A269411/b269411.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^5 + 5*n^4 + (11/2)*n^3 + n^2 - (1/2)*n.

%F Conjectures from _Colin Barker_, Jan 21 2019: (Start)

%F G.f.: 3*x*(4 + 29*x + 10*x^2 - 3*x^3) / (1 - x)^6.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

%F (End)

%e Some solutions for n=8:

%e ..0. .0. .2. .0. .2. .2. .6. .6. .3. .5. .8. .1. .5. .4. .2. .0

%e ..5. .5. .8. .1. .3. .5. .0. .3. .8. .6. .7. .2. .0. .2. .3. .8

%e ..8. .3. .6. .1. .0. .1. .5. .6. .7. .6. .0. .3. .5. .5. .0. .1

%e ..4. .0. .7. .0. .2. .5. .0. .5. .1. .7. .7. .4. .7. .6. .7. .8

%e ..5. .7. .0. .5. .3. .4. .4. .2. .7. .5. .8. .7. .7. .8. .8. .1

%Y Row 5 of A269409.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 25 2016