This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A071530 #23 May 26 2025 09:52:34
%S A071530 3,6,7,9,10,13,15,17,18,19,23,24,25,26,32,33,35,38,41,44,47,54,60,62,
%T A071530 68,69,74,80,83,89,95,99,110,113,119,128,179,194
%N A071530 Numbers that are the sum of 3 triangular numbers in exactly 2 ways.
%C A071530 If it is required that the triangular numbers be positive, sequence A064825 results. - _Jon E. Schoenfield_, Jan 01 2020
%F A071530 {n: A002636(n) =2}. - _R. J. Mathar_, May 26 2025
%e A071530 From _Jon E. Schoenfield_, Jan 01 2020: (Start)
%e A071530 15 is a term of the sequence because there are exactly 2 ways to express 15 as the sum of 3 triangular numbers: 15 = 6 + 6 + 3 = 15 + 0 + 0.
%e A071530 60 is a term because there are exactly 2 ways to express 60 as the sum of 3 triangular numbers: 60 = 36 + 21 + 3 = 45 + 15 + 0.
%e A071530 12 can be expressed as the sum of 3 triangular numbers in 3 ways, so it is not a term: 12 = 10 + 1 + 1 = 6 + 6 + 0 = 6 + 3 + 3. (End)
%t A071530 With[{max = 20}, t = Accumulate[Range[0, max]]; Select[Range[t[[-1]]], Length[IntegerPartitions[#, {3}, t]] == 2 &]] (* _Amiram Eldar_, May 14 2025 *)
%o A071530 (PARI) for(n=1,150,if(sum(i=0,n,sum(j=0,i,sum(k=0,j,if(i*(i+1)/2+j*(j+1)/2+k*(k+1)/2-n,0,1))))==2,print1(n,",")))
%Y A071530 Cf. A000217, A060773, A061262, A002636.
%Y A071530 Cf. A064825, A002097, A008443, A064816.
%K A071530 nonn
%O A071530 1,1
%A A071530 _Benoit Cloitre_, Jun 02 2002
%E A071530 More terms from _Vladeta Jovovic_, Jun 07 2002
%E A071530 Removed keyword "more" because this is probably finite. - _R. J. Mathar_, May 26 2025