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!)
A291718 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. 9
1, 4, 6, 8, 36, 44, 16, 120, 192, 276, 25, 300, 596, 1130, 2010, 36, 630, 1436, 3321, 6880, 16400, 49, 1176, 3024, 8272, 20600, 57564, 120940, 64, 2016, 5568, 17528, 49184, 159784, 380344, 1075344 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..36.

EXAMPLE

A configuration of 6 picked points from a 7 X 7 grid with a line (mirror) symmetry w.r.t. the line indicated by +++, and no point symmetry would be:

  o o o o o o o

  + X o X o o o

  X + o o o X o

  o o + o o o o

  X o o + o o o

  o o o o + o o

  o X o o o + o

So it would not contribute to the count of central symmetric configurations in A291717(27).

.

A configuration

  o o + o o o o

  o o + o o o o

  X o + o X o o

  + X # X + + +

  X o + o X o o

  o o + o o o o

  o o + o o o o

would contribute both to a(27) and to A291717(27), because besides being mirror symmetric w.r.t. the lines indicated by +++, it has also a central symmetry w.r.t the point indicated by #.

.

Triangle begins:

   1;

   4,    6;

   9,   36,   44;

  16,  120,  192,   276;

  25,  300,  596,  1130,  2010;

  36,  630, 1436,  3321,  6880,  16400;

  49, 1176, 3024,  8272, 20600,  57564, 120940;

  64, 2016, 5568, 17528, 49184, 159784, 380344, 1075344;

CROSSREFS

Cf. A090642, A098485, A098487, A291716, A291717, A292152, A292153, A292154, A292155, A292156.

Sequence in context: A227553 A108270 A019161 * A137026 A090938 A087271

Adjacent sequences:  A291715 A291716 A291717 * A291719 A291720 A291721

KEYWORD

nonn,tabl,more

AUTHOR

Hugo Pfoertner, Sep 08 2017

STATUS

approved

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 June 17 18:47 EDT 2021. Contains 345085 sequences. (Running on oeis4.)