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A097125 Number of noncongruent integer-sided tetrahedra with largest side n. 13
1, 4, 16, 45, 116, 254, 516, 956, 1669, 2760, 4379, 6676, 9888, 14219, 19956, 27421, 37062, 49143, 64272, 82888, 105629, 133132, 166090, 205223, 251624, 305861, 369247, 442695, 527417, 624483, 735777, 861885, 1005214, 1166797, 1348609 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Andrey Zabolotskiy, Table of n, a(n) for n = 1..1000 [Extracted from the Kurz link]
James East, Michael Hendriksen, and Laurence Park, On the enumeration of integer tetrahedra, arXiv:2112.00899 [math.CO], 2021.
Sascha Kurz, Enumeration of integral tetrahedra, J. Integer Seqs., 10 (2007), # 07.9.3.
Sascha Kurz, Enumeration of integral tetrahedra, arXiv:0804.1310 [math.CO], 2008.
MATHEMATICA
cmd3[d01_, d02_, d03_, d12_, d13_, d23s_] := Det[{{0, d01^2, d02^2, d03^2, 1}, {d01^2, 0, d12^2, d13^2, 1}, {d02^2, d12^2, 0, d23s, 1}, {d03^2, d13^2, d23s, 0, 1}, {1, 1, 1, 1, 0}}];
cmd30s = Sqrt /@ Solve[cmd3[d01, d02, d03, d12, d13, d23s] == 0, d23s][[;; , 1, 2]];
edgePermutations = PermutationList[#, 6] & /@ GroupElements@PermutationGroup[{Cycles[{{2, 4}, {3, 5}}], Cycles[{{1, 2}, {5, 6}}], Cycles[{{2, 3}, {4, 5}}]}];
canonical[dd_] := AllTrue[edgePermutations, OrderedQ[{dd[[#]], dd}] &];
a[d_] := Module[{s = 0, dd, uu}, Do[With[{roots = (cmd30s /. {d01 -> d})},
dd = Min[Floor /@ roots + 1]; uu = Min[Max[Ceiling /@ roots - 1], d];
Do[If[canonical[{d, d02, d03, d12, d13, d23}], s += 1], {d23, dd, uu}]],
{d02, Quotient[d, 2] + 1, d}, {d12, d + 1 - d02, d02}, {d03, d + 1 - d02, d02}, {d13, d + 1 - d03, d02}]; s];
Array[a, 10] (* Andrey Zabolotskiy, Apr 04 2024, after Kurz's Algorithm 1 *)
CROSSREFS
Sequence in context: A359073 A134139 A213501 * A213480 A306302 A159940
KEYWORD
nonn
AUTHOR
Sascha Kurz, Jul 26 2004
STATUS
approved

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Last modified April 20 00:58 EDT 2024. Contains 371798 sequences. (Running on oeis4.)