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

 

Logo

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!)
A233166 Number of n X 6 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs). 1

%I

%S 236,4096,278528,19922944,1543503872,133143986176,12919261626368,

%T 1389782697508864,161003686678495232,19527607984278470656,

%U 2430358531711233425408,306658673481347586064384

%N Number of n X 6 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).

%H R. H. Hardin, <a href="/A233166/b233166.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 192*a(n-1) - 8192*a(n-2) for n>3.

%F Conjectures from _Colin Barker_, Oct 09 2018: (Start)

%F G.f.: 4*x*(59 - 10304*x + 356352*x^2) / ((1 - 64*x)*(1 - 128*x)).

%F a(n) = 64^(n-1) * (2^n+60) for n>1.

%F (End)

%e Some solutions for n=2:

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

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

%Y Column 6 of A233168.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 05 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 December 2 20:25 EST 2021. Contains 349445 sequences. (Running on oeis4.)