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
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
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, Sep 05 2005
EXTENSIONS
Offset corrected by Arkadiusz Wesolowski, Aug 06 2012
STATUS
approved