

A085377


a(n) = 15n^2 + 13n^3.


2



0, 28, 164, 486, 1072, 2000, 3348, 5194, 7616, 10692, 14500, 19118, 24624, 31096, 38612, 47250, 57088, 68204, 80676, 94582, 110000, 127008, 145684, 166106, 188352, 212500, 238628, 266814, 297136, 329672, 364500, 401698, 441344, 483516, 528292
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OFFSET

0,2


COMMENTS

Numbers that are the sum of three solutions of the Diophantine equation x^3  y^3 = z^2.
Parametric representation of the solution is (x,y,z) = (8n^2, 7n^2, 13n^3), thus getting a(n) = 8n^2 + 7n^2 + 13n^3 = 15n^2 + 13n^3.
Geometrically, 13^2 = 8^3  7^3 means that the square of the hypotenuse of a Pythagorean triangle (5,12,13) is the difference of two cubes, which I recently found on p70 of David Wells' book "The Penguin Dictionary of Curios and Interesting Numbers", Penguin Books, 1997. See also A085479.


LINKS

Table of n, a(n) for n=0..34.


FORMULA

a(n)=4*a(n1)6*a(n2)+4*a(n3)a(n4). G.f.: 2*x*(14+26*xx^2)/(1x)^4. [From R. J. Mathar, Apr 20 2009]


MATHEMATICA

Table[15n^2 + 13n^3, {n, 1, 34}]


CROSSREFS

Cf. A085409.
Sequence in context: A184607 A215699 A220158 * A219298 A197967 A305270
Adjacent sequences: A085374 A085375 A085376 * A085378 A085379 A085380


KEYWORD

nonn


AUTHOR

Jun Mizuki (suzuki32(AT)sanken.osakau.ac.jp), Aug 12 2003


EXTENSIONS

More terms from Robert G. Wilson v, Aug 16 2003
Edited by N. J. A. Sloane, Apr 29 2008


STATUS

approved



