The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A279494 T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards. 7

%I #4 Dec 13 2016 12:22:14

%S 0,1,1,0,0,0,3,5,5,3,3,18,38,18,3,9,68,254,254,68,9,15,235,1433,2684,

%T 1433,235,15,31,801,8330,26157,26157,8330,801,31,57,2678,46095,246237,

%U 425588,246237,46095,2678,57,108,8777,250440,2241332,6559816,6559816

%N T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

%C Table starts

%C ...0.....1.......0..........3............3..............9...............15

%C ...1.....0.......5.........18...........68............235..............801

%C ...0.....5......38........254.........1433...........8330............46095

%C ...3....18.....254.......2684........26157.........246237..........2241332

%C ...3....68....1433......26157.......425588........6559816.........98128162

%C ...9...235....8330.....246237......6559816......166229033.......4065077852

%C ..15...801...46095....2241332.....98128162.....4065077852.....162346342126

%C ..31..2678..250440...19885341...1427793365....96674459373....6294925767121

%C ..57..8777.1332366..172968364..20331614084..2247110811000..238434528280477

%C .108.28343.6989712.1481176019.284582186755.51300573165630.8863487201716422

%H R. H. Hardin, <a href="/A279494/b279494.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

%F k=1: a(n) = 3*a(n-1) -5*a(n-3) +3*a(n-5) +a(n-6)

%F k=2: [order 16]

%F k=3: [order 54] for n>55

%e Some solutions for n=4 k=4

%e ..0..1..1..1. .0..1..1..0. .0..1..0..1. .0..1..1..1. .0..1..1..1

%e ..0..1..0..1. .0..0..1..0. .1..1..0..1. .1..0..1..0. .1..0..0..1

%e ..0..1..0..0. .0..0..1..0. .0..1..0..1. .1..0..1..1. .0..1..1..0

%e ..0..1..0..1. .1..0..1..0. .1..1..1..0. .0..1..0..1. .0..0..1..1

%Y Column 1 is A105423(n-2).

%K nonn,tabl

%O 1,7

%A _R. H. Hardin_, Dec 13 2016

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 29 18:36 EDT 2024. Contains 372952 sequences. (Running on oeis4.)