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A112352 Triangular numbers that are the sum of two distinct positive triangular numbers. 2
21, 36, 55, 66, 91, 120, 136, 171, 231, 276, 351, 378, 406, 496, 561, 666, 703, 741, 820, 861, 946, 990, 1035, 1081, 1176, 1225, 1326, 1378, 1431, 1485, 1540, 1596, 1653, 1711, 1770, 1891, 1953, 2016, 2080, 2211, 2278, 2346, 2556, 2701, 2775, 2850, 2926 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A089982: it doesn't require the two positive triangular numbers to be distinct.

Subsequence of squares: 36, 1225, 41616, 1413721,... is also in A001110. - Zak Seidov, May 07 2015

First term with 2 representations is 231: 21+210=78+153, first term with 3 representations is 276: 45+211=66+120=105+171; apparently the number of representations is unbounded. - Zak Seidov, May 11 2015

LINKS

Zak Seidov, Table of n, a(n) for n = 1..1000

EXAMPLE

36 is a term because 36 = 15 + 21 and these three numbers are distinct triangular numbers (A000217(8) = A000217(5) + A000217(6)).

MAPLE

N:= 10^5: # to get all terms <= N

S:= {}:

for a from 1 to floor(sqrt(1+8*N)/2) do

  for b from 1 to a-1 do

    y:= a*(a+1)/2 + b*(b+1)/2;

      if y > N then break fi;

      if issqr(8*y+1) then S:= S union {y} fi

  od

od:

sort(convert(S, list)); # Robert Israel, May 13 2015

MATHEMATICA

Select[Union[Total/@Subsets[Accumulate[Range[100]], {2}]], OddQ[ Sqrt[ 1+8#]]&] (* Harvey P. Dale, Feb 28 2016 *)

CROSSREFS

Cf. A000217 (triangular numbers), A112353 (triangular numbers that are the sum of three distinct positive triangular numbers), A089982.

Cf. A001110. - Zak Seidov, May 07 2015

Sequence in context: A219215 A155710 A001491 * A298472 A168513 A067598

Adjacent sequences:  A112349 A112350 A112351 * A112353 A112354 A112355

KEYWORD

nonn

AUTHOR

Rick L. Shepherd, Sep 05 2005

EXTENSIONS

Offset corrected by Arkadiusz Wesolowski, Aug 06 2012

STATUS

approved

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Last modified April 26 08:05 EDT 2019. Contains 322472 sequences. (Running on oeis4.)