A133215 Hexagonal numbers (A000384) which are sum of 2 other hexagonal numbers > 0.

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

Offset

1,1

Comments

This is to A136117 as A000384 is to A000326. Duke and Schulze-Pillot (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

Donovan Johnson, Table of n, a(n) for n = 1..1000

W. Duke and R. Schulze-Pilot, Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids, Invent. Math. 99(1990), 49-57.

Eric Weisstein's World of Mathematics, Hexagonal Number.

Formula

{x: x>0 and x in A000384 and x = A000384(i) + A000384(j) for i>0 and j>0}, where A000384 = {n*(2*n-1) for n > 0}.

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(2n-1), {n, Ceiling[ (1+Sqrt[1+8upto])/4]}], {2}]], IntegerQ[(1+Sqrt[1+8#])/4]&&#<=upto&]] (* Harvey P. Dale, Jul 24 2011 *)

Crossrefs

Cf. A000384, A136117.

Sequence in context: A008892 A216072 A284277 * A343426 A015232 A128382

Adjacent sequences: A133212 A133213 A133214 * A133216 A133217 A133218

Keyword

nonn

Author

Jonathan Vos Post, Dec 18 2007

Extensions

Added missing term 276 and a(8)-a(35) from Donovan Johnson, Sep 27 2008

Status

approved