A135796 Numbers of the form 4x^3y+4y x^3 (where x,y are positive integers).

8, 40, 120, 128, 272, 312, 520, 640, 648, 888, 1160, 1200, 1400, 1920, 2040, 2048, 2080, 2952, 2968, 3240, 3280, 4040, 4352, 4872, 4992, 5000, 5368, 6120, 6960, 7008, 7280, 7320, 8320, 8840, 9720

Offset

1,1

Comments

Squares of these numbers are of the form N^4-M^2 (where N belongs to A135786 and M to A135797) Proof uses: (4x^3y+4xy^3)^2=(x^2-y^2)^4+(x^4+6x^2y^2+y^4)^2.

Refers to A057102, which had an incorrect description and has been replaced by A256418. As a result the present sequence should be re-checked. - N. J. A. Sloane, Apr 06 2015

Links

Table of n, a(n) for n=1..35.

Mathematica

a = {}; Do[Do[w = 4x^3y + 4x y^3; If[w < 10000, AppendTo[a, w]], {x, y, 1000}], {y, 1, 1000}]; Union[a] (*Artur Jasinski*)

Crossrefs

Cf. A000404, A050803, A057102, A135784, A060803, A135786, A135787, A135789, A135790, A135791, A135792, A135793, A135795, A135796, A135797.

Sequence in context: A211631 A279273 A143943 * A105374 A162668 A227733

Adjacent sequences: A135793 A135794 A135795 * A135797 A135798 A135799

Keyword

nonn

Author

Artur Jasinski, Nov 29 2007

Status

approved