A262749 Numbers that are the sum of two distinct nonzero triangular numbers in more than one way.

16, 31, 46, 51, 76, 81, 94, 106, 111, 121, 123, 126, 133, 141, 146, 156, 157, 172, 174, 181, 186, 191, 196, 198, 211, 216, 225, 226, 231, 237, 241, 246, 256, 259, 268, 276, 281, 286, 289, 291, 297, 301, 310, 315, 321, 326, 328, 331, 336, 346, 354, 361, 366

Offset

1,1

Comments

The magic sum of any 3 X 3 semimagic square composed of triangular numbers is a(n) + A000217(m) for some m and n.

Links

Table of n, a(n) for n=1..53.

Example

16 = 1 + 15 = 6 + 10.

Mathematica

r = 366; lst = Table[0, {r}]; lim = Floor[Sqrt[8*r - 7]]; Do[num = (i^2 + i)/2 + (j^2 + j)/2; If[num <= r, lst[[num]]++], {i, lim}, {j, i - 1}]; Flatten@Position[lst, n_ /; n > 1]
Module[{nn=30, trnos}, trnos=Accumulate[Range[nn]]; Select[Sort[Flatten[ Table[ PositionIndex[Counts[Total/@Subsets[trnos, {2}]]][i], {i, 2, nn}]]], #<= Last[trnos]&]] (* The program uses the PositionIndex and Counts functions from Mathematica version 10 *)  (* Harvey P. Dale, Dec 26 2015 *)

Crossrefs

Cf. A000217, A051533, A260647, A265140 (exactly one way), A265134 (exactly two ways), A265135 (more than two ways), A265136 (exactly three ways), A265137 (more than three ways), A265138 (exactly four ways).

Sequence in context: A185979 A185980 A064816 * A265134 A220000 A132299

Adjacent sequences: A262746 A262747 A262748 * A262750 A262751 A262752

Keyword

nonn

Author

Arkadiusz Wesolowski, Dec 02 2015

Status

approved