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!)
A292156 Triangle T(m,k) read by rows, where T(m,k) is the number of ways in which 1<=k<=m positions can be picked in an m X m square grid such that the picked positions have a line symmetry but no point symmetry. 9

%I #13 Sep 20 2017 05:09:19

%S 0,0,0,0,0,36,0,0,168,220,0,0,524,944,1960,0,0,1292,2848,6752,15752,0,

%T 0,2736,7248,20280,55904,120212,0,0,5088,15576,48576,156224,378824,

%U 1068008

%N Triangle T(m,k) read by rows, where T(m,k) is the number of ways in which 1<=k<=m positions can be picked in an m X m square grid such that the picked positions have a line symmetry but no point symmetry.

%F a(n) = A292153(n) - A291717(n) = A291718(n) - A292154(n).

%e The triangle begins:

%e 0;

%e 0, 0;

%e 0, 0, 36;

%e 0, 0, 168, 220;

%e 0, 0, 524, 944, 1960;

%e 0, 0, 1292, 2848, 6752, 15752;

%e 0, 0, 2736, 7248, 20280, 55904, 120212;

%e .

%e The following configuration of 6 picked points from a 7X7 grid with a line (mirror) symmetry w.r.t. the line indicated by +++, but no point symmetry, is one of the T(7,6)=a(27)=55904 configurations with this property:

%e o o o o o o o

%e + X o X o o o

%e X + o o o X o

%e o o + o o o o

%e X o o + o o o

%e o o o o + o o

%e o X o o o + o

%Y Cf. A090642, A098485, A098487, A291716, A291717, A291718, A292152, A292153, A292154, A292155.

%K nonn,tabl,more

%O 1,6

%A _Hugo Pfoertner_, Sep 17 2017

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 March 29 20:01 EDT 2024. Contains 371281 sequences. (Running on oeis4.)