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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

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;

CROSSREFS

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

Sequence in context: A296570 A241667 A259258 * A022899 A081148 A306954

Adjacent sequences:  A291713 A291714 A291715 * A291717 A291718 A291719

KEYWORD

nonn,tabl,more

AUTHOR

Hugo Pfoertner, Sep 08 2017

STATUS

approved

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Last modified June 13 12:42 EDT 2021. Contains 344996 sequences. (Running on oeis4.)