1,1

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.

Duke, W. and Schulze-Pillot, R. "Representations of Integers by Positive Ternary Quadratic Forms and Equidistribution of Lattice Points on Ellipsoids." Invent. Math. 99, 49-57, 1990.

Eric Weisstein's World of Mathematics, Hexagonal Number.

{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}.

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).

Cf. A000384, A136117.

Sequence in context: A140433 A035852 A045146 this_sequence A083735 A105846 A091553

Adjacent sequences: A133212 A133213 A133214 this_sequence A133216 A133217 A133218

more,nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Dec 18 2007