A064828 Numbers which are the sum of two positive triangular numbers in exactly three different ways.

81, 106, 156, 181, 211, 256, 276, 331, 361, 381, 406, 456, 556, 606, 631, 666, 681, 706, 718, 731, 781, 856, 861, 931, 939, 956, 981, 1051, 1131, 1206, 1231, 1406, 1456, 1506, 1563, 1606, 1631, 1681, 1731, 1732, 1756, 1831, 1891, 1901, 1956, 1981, 2081

Offset

1,1

Links

Harry J. Smith, Table of n, a(n) for n = 1..500

Example

81 = 45 + 36 = 66 + 15 = 78 + 3.

Mathematica

Take[Transpose[Select[Split[Sort[Total/@(Union[Sort/@Tuples[Accumulate[ Range[300]], {2}]])]], Length[#]==3&]][[1]], 60] (* Harvey P. Dale, Jun 04 2011 *)

Prog

(PARI) Tri(n)= { n*(n + 1)/2 } { n=0; for (m=1, 10^9, k=0; i=1; until (t>=m\2 || k>3, t=Tri(i); j=i; i++; until (s>=m || k>3, s=t + Tri(j); j++; if (s==m, k++))); if (k==3, write("b064828.txt", n++, " ", m); if (n==1000, return)) ) } [Harry J. Smith, Sep 27 2009]

Crossrefs

Cf. A000217, A064816.

Sequence in context: A256349 A202002 A249613 * A265135 A265136 A120457

Adjacent sequences: A064825 A064826 A064827 * A064829 A064830 A064831

Keyword

nonn

Author

Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 23 2001

Status

approved