OFFSET
1,2
COMMENTS
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).
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.
LINKS
Giovanni Corbelli, Table of n, a(n) for n = 1..254
Sascha Kurz, Enumeration of integral tetrahedra, arXiv:0804.1310 [math.CO], 2008.
CROSSREFS
KEYWORD
nonn
AUTHOR
Giovanni Corbelli, Nov 13 2021
STATUS
approved