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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. Sascha Kurz, Number of integral tetrahedra with given diameter, 2007. 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 Cf. A000065, A002620, A097126, A097127, A208454, A349295, A349296, A371344, A371345. Sequence in context: A359073 A134139 A213501 * A213480 A306302 A159940 Adjacent sequences: A097122 A097123 A097124 * A097126 A097127 A097128 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.)