

A133215


Hexagonal numbers (A000384) which are sum of 2 other hexagonal numbers > 0.


2



276, 703, 861, 1225, 2850, 3003, 4560, 5151, 8128, 10878, 11781, 12090, 12720, 13366, 14706, 15400, 16110, 18721, 21115, 22366, 24090, 24531, 26796, 29161, 29646, 31125, 32131, 33153, 36315, 38503, 39621, 40186, 42486, 45451, 47895
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OFFSET

1,1


COMMENTS

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.


LINKS



FORMULA



EXAMPLE

hex(19) = 703 = 378 + 325 = hex(14) + hex(13).
hex(21) = 861 = 630 + 231 = hex(18) + hex(11).
hex(25) = 1225 = 1035 + 190 = hex(23) + hex(10).
hex(38) = 2850 = 2415 + 435 = hex(35) + hex(15).
hex(39) = 3003 = 2850 + 153 = hex(38) + hex(9) = 2415 + 435 + 153 = hex(35) + hex(15) + hex(9).
hex(48) = 4560 = 2415 + 2145 = hex(35) + hex(33).


MATHEMATICA

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 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



