%I
%S 276,703,861,1225,2850,3003,4560,5151,8128,10878,11781,12090,12720,
%T 13366,14706,15400,16110,18721,21115,22366,24090,24531,26796,29161,
%U 29646,31125,32131,33153,36315,38503,39621,40186,42486,45451,47895
%N Hexagonal numbers (A000384) which are sum of 2 other hexagonal numbers > 0.
%C This is to A136117 as A000384 is to A000326. Duke and SchulzePillot (1990) proved that every sufficiently large integer (and hence every sufficiently large hexagonal number) can be written as the sum of three hexagonal numbers.
%H Donovan Johnson, <a href="/A133215/b133215.txt">Table of n, a(n) for n = 1..1000</a>
%H W. Duke and R. SchulzePilot, <a href="http://gdz.sub.unigoettingen.de/dms/load/img/?PID=GDZPPN002107066">Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids</a>, Invent. Math. 99(1990), 4957.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HexagonalNumber.html">Hexagonal Number</a>.
%F {x: x>0 and x in A000384 and x = A000384(i) + A000384(j) for i>0 and j>0}, where A000384 = {n*(2*n1) for n > 0}.
%e hex(19) = 703 = 378 + 325 = hex(14) + hex(13).
%e hex(21) = 861 = 630 + 231 = hex(18) + hex(11).
%e hex(25) = 1225 = 1035 + 190 = hex(23) + hex(10).
%e hex(38) = 2850 = 2415 + 435 = hex(35) + hex(15).
%e hex(39) = 3003 = 2850 + 153 = hex(38) + hex(9) = 2415 + 435 + 153 = hex(35) + hex(15) + hex(9).
%e hex(48) = 4560 = 2415 + 2145 = hex(35) + hex(33).
%t With[{upto=60000},Select[Union[Total/@Subsets[Table[n(2n1),{n, Ceiling[ (1+Sqrt[1+8upto])/4]}],{2}]],IntegerQ[(1+Sqrt[1+8#])/4]&&#<=upto&]] (* _Harvey P. Dale_, Jul 24 2011 *)
%Y Cf. A000384, A136117.
%K nonn
%O 1,1
%A _Jonathan Vos Post_, Dec 18 2007
%E Added missing term 276 and a(8)a(35) from _Donovan Johnson_, Sep 27 2008
