A269691 - OEIS

%I #7 Jan 28 2019 09:00:25

%S 24,201,944,2995,7584,16541,32416,58599,99440,160369,248016,370331,

%T 536704,758085,1047104,1418191,1887696,2474009,3197680,4081539,

%U 5150816,6433261,7959264,9761975,11877424,14344641,17205776,20506219,24294720

%N Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by plus or minus one modulo n+1.

%H R. H. Hardin, <a href="/A269691/b269691.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^5 + 5*n^4 + 10*n^3 + 4*n^2 - 3*n - 1 for n>1.

%F Conjectures from _Colin Barker_, Jan 28 2019: (Start)

%F G.f.: x*(24 + 57*x + 98*x^2 - 134*x^3 + 114*x^4 - 47*x^5 + 8*x^6) / (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>7.

%F (End)

%e Some solutions for n=3:

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

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

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

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

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

%Y Row 5 of A269690.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 03 2016