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A291716
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 center of gravity of the k picked positions coincides with one of the picked positions.
9
1, 4, 0, 9, 0, 8, 16, 0, 24, 44, 25, 0, 72, 176, 610, 36, 0, 144, 660, 2996, 12092, 49, 0, 288, 1788, 11492, 64648, 323940, 64, 0, 480, 4116, 35676, 269924, 1811696, 10866196
OFFSET
1,2
EXAMPLE
T(3,3) = a(6) = 8 because there are the following 8 ways to pick 3 positions such that one of them is the center of gravity of the other two.
XXX...ooo...ooo...Xoo...oXo...ooX...Xoo...ooX
ooo...XXX...ooo...Xoo...oXo...ooX...oXo...oXo
ooo...ooo...XXX...Xoo...oXo...ooX...ooX...Xoo
.
An example of one of the T(4,4)=a(10)=44 "balanced" configurations is
x.o.o.x
o.o.X.o
o.o.o.o
o.o.o.x
X is at the center of gravity of the 3 other picked positions x.
.
Triangle begins:
1;
4, 0;
9, 0, 8;
16, 0, 24, 44;
25, 0, 72, 176, 610;
36, 0, 144, 660, 2996, 12092;
49, 0, 288, 1788, 11492, 64648, 323940;
64, 0, 480, 4116, 35676, 269924, 1811696, 10866196;
KEYWORD
nonn,tabl,more
AUTHOR
Hugo Pfoertner, Sep 08 2017
STATUS
approved