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.

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

Author

Hugo Pfoertner, Sep 08 2017

Keywords

• nonn
• tabl
• more

Examples

			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;
		

Crossrefs

Cf. A090642, A098485, A098487, A291717, A291718, A292152, A292153, A292154, A292155, A292156.