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A262749
Numbers that are the sum of two distinct nonzero triangular numbers in more than one way.
9
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.
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
KEYWORD
nonn
AUTHOR
STATUS
approved