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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.
5
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
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
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
KEYWORD
nonn
AUTHOR
Rainer Rosenthal, Apr 20 2022
EXTENSIONS
a(23) and beyond from Hugo Pfoertner, Apr 20 2022
STATUS
approved