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A292152 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 don't have any symmetry. 9
0, 0, 0, 0, 0, 40, 0, 0, 368, 1432, 0, 0, 1704, 10992, 50992, 0, 0, 5704, 53784, 369776, 1925464, 0, 0, 15400, 198696, 1885128, 13903624, 85773968, 0, 0, 36096, 606264, 7572896, 74743584, 620821688, 4424756040 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,6

REFERENCES

Walter Krämer, Denkste! Trugschlüsse aus der Welt der Zahlen und des Zufalls. Campus Verlag, Frankfurt/Main, 1996. Chapter 4, pp. 71-82.

LINKS

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

FORMULA

a(n) = A090642(n) - A292153(n).

EXAMPLE

The triangle begins:

  0;

  0,  0;

  0,  0,    40;

  0,  0,   368,   1432;

  0,  0,  1704,  10992,  50992;

  0,  0,  5704,  53784,  369776,  1925464;

  0,  0, 15400, 198696, 1885128, 13903624, 85773968;

.

The following configuration of 6 picked points from a 7X7 grid is one of the T(7,6)=a(28)=13903624 configurations without symmetry. It is of some historical interest, because when it was drawn in Germany's "Lotto 6 aus 49", there was only one person with a winning bet receiving a payout of 22 million DM (Deutsche Mark).

.

  o o o o o o o

  o o o o o o o

  o o o o X o o

  o o X o o o o

  o o o o o o X

  X X X o o o o

  o o o o o o o

CROSSREFS

Cf. A090642, A098485, A098487, A291716, A291717, A291718, A292153, A292154, A292155, A292156.

Sequence in context: A173364 A023931 A067159 * A331907 A247404 A013373

Adjacent sequences:  A292149 A292150 A292151 * A292153 A292154 A292155

KEYWORD

nonn,tabl,more

AUTHOR

Hugo Pfoertner, Sep 17 2017

STATUS

approved

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Last modified June 13 18:45 EDT 2021. Contains 345008 sequences. (Running on oeis4.)