login
A292154
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 both a point symmetry and a line symmetry.
9
1, 4, 6, 9, 36, 8, 16, 120, 24, 56, 25, 300, 72, 186, 50, 36, 630, 144, 473, 128, 648, 49, 1176, 288, 1024, 320, 1660, 728, 64, 2016, 480, 1952, 608, 3560, 1520, 7326
OFFSET
1,2
FORMULA
a(n) = A292153(n) - A292155(n) - A292156(n).
a(n) = A291717(n) - A292155(n).
a(n) = A291718(n) - A292156(n).
EXAMPLE
The triangle begins:
1;
4, 6;
9, 36, 8;
16, 120, 24, 56;
25, 300, 72, 186, 50;
36, 630, 144, 473, 128, 648;
49, 1176, 288, 1024, 320, 1660, 728;
64, 2016, 480, 1952, 608, 3560, 1520, 7326;
.
o o o o o o
X o o X o o
o o o o o o
X o o X o o
o o o o o o
X o o X o o
is one of the T(6,6)=a(21)=648 configurations with both types of symmetry.
.
o o X o o o
o X o o o o
o o o X o o
o o o o o X
o o o o X o
o o o o o o
is one of the T(6,5)=a(20)=128 configurations with both types of symmetry.
KEYWORD
nonn,tabl,more
AUTHOR
Hugo Pfoertner, Sep 17 2017
STATUS
approved