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A292155 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 point symmetry but no line symmetry. 9
0, 0, 0, 0, 0, 0, 0, 0, 0, 112, 0, 0, 0, 528, 128, 0, 0, 0, 1800, 336, 5928, 0, 0, 0, 4908, 1156, 22628, 5676, 0, 0, 0, 11584, 2432, 71000, 14160, 333994 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,10

REFERENCES

Walter Krämer, Denkste! Trugschlüsse aus der Welt der Zahlen und des Zufalls. Campus Verlag, Frankfurt/Main, 1996.

LINKS

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

FORMULA

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

EXAMPLE

The triangle begins:

   0;

   0, 0;

   0, 0, 0;

   0, 0, 0,   112;

   0, 0, 0,   528,  128;

   0, 0, 0,  1800,  336,  5928;

   0, 0, 0,  4908, 1156, 22628,  5676;

   0, 0, 0, 11584, 2432, 71000, 14160, 333994;

.

The following configuration of 6 picked points from a 7X7 grid with a point symmetry but no line (mirror) symmetry is one of the T(7,6)=a(28)=22628 configurations with this property. It is of some historical interest, because when it was drawn in Germany's "Lotto 6 aus 49" in January 1988, there were 222 persons instead of typically 5-10 with a winning bet. They only won 31000 DM (Deutsche Mark) instead of the 1 million DM they had hoped for.

.

  o o o o o o o

  o o o o o o o

  o o o o o o o

  o o X X X o o

  o X X X o o o

  o o o o o o o

  o o o o o o o

.

The shown configuration is also in A098485(28) (graph consisting of a single component).

CROSSREFS

Cf. A090642, A098485, A098487, A291716, A291717, A291718, A292152, A292153, A292154, A292156.

Sequence in context: A261820 A262661 A156407 * A341011 A103849 A340470

Adjacent sequences:  A292152 A292153 A292154 * A292156 A292157 A292158

KEYWORD

nonn,tabl,more

AUTHOR

Hugo Pfoertner, Sep 17 2017

STATUS

approved

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Last modified June 24 20:35 EDT 2021. Contains 345425 sequences. (Running on oeis4.)