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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
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.
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).
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KEYWORD
nonn,tabl,more
AUTHOR
Hugo Pfoertner, Sep 17 2017
STATUS
approved