A353447 a(n) is the number of tetrapods standing on the four edges of an n X n grid, so that no two feet are the same distance apart and no foot is on a corner. Tetrapods with congruent footprints are counted only once.

0, 0, 1, 11, 40, 105, 190, 379, 616, 987, 1426, 2139, 2964, 4130, 5403, 7180, 9155, 11716, 14458, 18092, 22037, 26808, 31793, 38343, 45060, 53184, 61613, 71878, 82466, 95368, 108195, 123790, 140040, 158457, 177405, 200020, 223039, 248769, 275214, 306411, 337645

Offset

3,4

Comments

If we name the tetrapod's footprints "mini-frame", we can say that mini-frames span their grid, i.e., there is no smaller grid for them. Every corner-less set of points with distinct distances in a smallest possible n X n grid contains at least one mini-frame.

Links

Hugo Pfoertner, Table of n, a(n) for n = 3..200

Example

  .
     . C .           a(3) = 0              . . . C .
     D . B   <===  since AB = CD           . . . . .
     . A .         is forbidden            . . . . B
                                           . . . . .
                        . C . .            D . . . .
      a(4) = 0  ===>    ? . . .            . A . . .
    (there is no        ? . . B         ______________
     space for D)       . A . .            a(5) = 1
                                     (No other solutions)
  .
    . . . . .           The tetrapod has 6 distinct
    D . . . .           squared distances 4, 5, 10,
    . . . . C   <=====  13, 17, 18, but it uses only
    . . . . .           three edges of the 5 X 5 grid.
    . A . B .           (Not allowed.)
  .

Crossrefs

Cf. A193838, A271490, A335232, A351699, A351700, A353532.

The general case without excluding the corners of the grid rectangle is covered in A354700 and A354701.

Sequence in context: A031427 A147296 A337130 * A059142 A064798 A056124

Adjacent sequences: A353444 A353445 A353446 * A353448 A353449 A353450

Keyword

nonn

Author

Rainer Rosenthal, Apr 20 2022

Extensions

a(23) and beyond from Hugo Pfoertner, Apr 20 2022

Status

approved