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%I #27 Dec 17 2024 08:45:42
%S 81,106,156,181,211,256,276,331,361,381,406,456,556,606,631,666,681,
%T 706,718,731,781,856,861,931,939,956,981,1051,1131,1206,1231,1406,
%U 1456,1506,1563,1606,1631,1681,1731,1732,1756,1831,1891,1901,1956,1981,2081
%N Numbers which are the sum of two positive triangular numbers in exactly three different ways.
%H Harry J. Smith, <a href="/A064828/b064828.txt">Table of n, a(n) for n = 1..500</a>
%e 81 = 45 + 36 = 66 + 15 = 78 + 3.
%t Take[Transpose[Select[Split[Sort[Total/@(Union[Sort/@Tuples[Accumulate[ Range[300]],{2}]])]],Length[#]==3&]][[1]],60] (* _Harvey P. Dale_, Jun 04 2011 *)
%o (PARI) isok(n)={ my(k=0,i=1,t=1); while (t<=n\2 && k<=3, if(ispolygonal(n-t,3), k++); i++; t+=i); k==3 } \\ _Harry J. Smith_, Sep 27 2009
%Y Cf. A000217, A064816.
%K nonn
%O 1,1
%A Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 23 2001