

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
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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 510 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



