

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
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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 a1 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



