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%I #10 Apr 21 2024 19:21:24
%S 1,14,109,479,1570,4031,8997,17948,32853,56408,91776,143003,215196,
%T 313732,444813,616816,839685,1120435,1472736,1907995,2440463,3086644,
%U 3861599,4784197,5878808,7160841,8659826,10399512,12407231,14710254,17351756
%N First differences of A349295.
%C a(n) is the number of ordered 6-tuples (a_1,a_2,a_3,a_4,a_5,a_6) having all terms in {1,...,n}, with at least one element equal to n, such that there exists a tetrahedron ABCD with those edge-lengths, taken in a particular order (see comments in A349295).
%C Conjecture: for n tending to infinity the ratio a(n) / A097125(n) tends to 24 as the probability that all a_i's are different tends to 1 and there are 24 6-tuples corresponding to the same tetrahedron if all a_i's are different. For n=254 the ratio is 23.9936919.
%H Giovanni Corbelli, <a href="/A349296/b349296.txt">Table of n, a(n) for n = 1..254</a>
%H Sascha Kurz, <a href="http://arxiv.org/abs/0804.1310">Enumeration of integral tetrahedra</a>, arXiv:0804.1310 [math.CO], 2008.
%Y Cf. A097125, A349295.
%K nonn
%O 1,2
%A _Giovanni Corbelli_, Nov 13 2021
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