A269608 - OEIS

%I #8 Jan 25 2019 08:29:09

%S 10,154,804,2692,7030,15630,31024,56584,96642,156610,243100,364044,

%T 528814,748342,1035240,1403920,1870714,2453994,3174292,4054420,

%U 5119590,6397534,7918624,9715992,11825650,14286610,17141004,20434204,24214942

%N Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by one or less.

%H R. H. Hardin, <a href="/A269608/b269608.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^5 + 5*n^4 + 7*n^3 - 4*n^2 + n.

%F Conjectures from _Colin Barker_, Jan 25 2019: (Start)

%F G.f.: 2*x*(5 + 47*x + 15*x^2 - 11*x^3 + 4*x^4) / (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=7:

%e ..2. .3. .4. .7. .7. .4. .6. .7. .1. .2. .6. .4. .1. .2. .4. .5

%e ..6. .2. .7. .5. .3. .3. .4. .7. .4. .1. .0. .6. .5. .4. .2. .6

%e ..1. .5. .1. .4. .6. .1. .5. .5. .2. .0. .7. .4. .3. .0. .0. .1

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

%e ..7. .3. .5. .5. .4. .7. .3. .3. .2. .2. .1. .2. .6. .1. .2. .0

%Y Row 5 of A269606.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 01 2016