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A349296 First differences of A349295. 3
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 (list; graph; refs; listen; history; text; internal format)
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 from a(n) and the corresponding a(n) in A097125 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
Sascha Kurz, Enumeration of integral tetrahedra, arXiv:0804.1310 [math.CO], 2008.
CROSSREFS
Sequence in context: A181378 A020327 A039629 * A205493 A074886 A294445
KEYWORD
nonn
AUTHOR
Giovanni Corbelli, Nov 13 2021
STATUS
approved

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Last modified April 18 16:22 EDT 2024. Contains 371780 sequences. (Running on oeis4.)