A349296 First differences of A349295.

1, 14, 109, 479, 1570, 4031, 8997, 17948, 32853, 56408, 91776, 143003, 215196, 313732, 444813, 616816, 839685, 1120435, 1472736, 1907995, 2440463, 3086644, 3861599, 4784197, 5878808, 7160841, 8659826, 10399512, 12407231, 14710254, 17351756

Offset: 1

Author

Giovanni Corbelli, Nov 13 2021

Keywords

• nonn

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

Cf. A097125, A349295.