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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.

%I A353447 #25 Jun 11 2022 05:51:15
%S A353447 0,0,1,11,40,105,190,379,616,987,1426,2139,2964,4130,5403,7180,9155,
%T A353447 11716,14458,18092,22037,26808,31793,38343,45060,53184,61613,71878,
%U A353447 82466,95368,108195,123790,140040,158457,177405,200020,223039,248769,275214,306411,337645
%N 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.
%C A353447 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.
%H A353447 Hugo Pfoertner, <a href="/A353447/b353447.txt">Table of n, a(n) for n = 3..200</a>
%e A353447   .
%e A353447      . C .           a(3) = 0              . . . C .
%e A353447      D . B   <===  since AB = CD           . . . . .
%e A353447      . A .         is forbidden            . . . . B
%e A353447                                            . . . . .
%e A353447                         . C . .            D . . . .
%e A353447       a(4) = 0  ===>    ? . . .            . A . . .
%e A353447     (there is no        ? . . B         ______________
%e A353447      space for D)       . A . .            a(5) = 1
%e A353447                                      (No other solutions)
%e A353447   .
%e A353447     . . . . .           The tetrapod has 6 distinct
%e A353447     D . . . .           squared distances 4, 5, 10,
%e A353447     . . . . C   <=====  13, 17, 18, but it uses only
%e A353447     . . . . .           three edges of the 5 X 5 grid.
%e A353447     . A . B .           (Not allowed.)
%e A353447   .
%Y A353447 Cf. A193838, A271490, A335232, A351699, A351700, A353532.
%Y A353447 The general case without excluding the corners of the grid rectangle is covered in A354700 and A354701.
%K A353447 nonn
%O A353447 3,4
%A A353447 _Rainer Rosenthal_, Apr 20 2022
%E A353447 a(23) and beyond from _Hugo Pfoertner_, Apr 20 2022