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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A221516 Number of 0..n arrays of length 5 with each element differing from at least one neighbor by 2 or more, starting with 0. 1

%I

%S 0,3,30,130,381,884,1765,3174,5285,8296,12429,17930,25069,34140,45461,

%T 59374,76245,96464,120445,148626,181469,219460,263109,312950,369541,

%U 433464,505325,585754,675405,774956,885109,1006590,1140149,1286560

%N Number of 0..n arrays of length 5 with each element differing from at least one neighbor by 2 or more, starting with 0.

%C Row 5 of A221515.

%H R. H. Hardin, <a href="/A221516/b221516.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 1*n^4 - 1*n^3 - 10*n^2 + 33*n - 34 for n>3.

%F Conjectures from _Colin Barker_, Aug 06 2018: (Start)

%F G.f.: x^2*(3 + 15*x + 10*x^2 + x^3 - 6*x^4 + 2*x^5 - x^6) / (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>8.

%F (End)

%e Some solutions for n=6:

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

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

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

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

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

%Y Cf. A221515.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 18 2013

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 24 03:22 EST 2020. Contains 332195 sequences. (Running on oeis4.)