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

1,2

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

Cf. A097125, A349295.

Sequence in context: A181378 A020327 A039629 * A205493 A074886 A294445

Adjacent sequences: A349293 A349294 A349295 * A349297 A349298 A349299

Keyword

nonn

Author

Giovanni Corbelli, Nov 13 2021

Status

approved