The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A269642 Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1. 1

%I

%S 12,159,796,2637,6876,15307,30444,55641,95212,154551,240252,360229,

%T 523836,741987,1027276,1394097,1858764,2439631,3157212,4034301,

%U 5096092,6370299,7887276,9680137,11784876,14240487,17089084,20376021,24150012

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

%H R. H. Hardin, <a href="/A269642/b269642.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^5 + 5*n^4 + 4*n^3 + 6*n^2 - 5*n + 1.

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

%F G.f.: x*(12 + 87*x + 22*x^2 + 6*x^3 - 6*x^4 - x^5) / (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=3:

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

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

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

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

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

%Y Row 5 of A269640.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 02 2016

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 2 20:25 EST 2021. Contains 349445 sequences. (Running on oeis4.)