A165220 Numbers n such that 8*n+1 is a cube.

0, 91, 614, 1953, 4492, 8615, 14706, 23149, 34328, 48627, 66430, 88121, 114084, 144703, 180362, 221445, 268336, 321419, 381078, 447697, 521660, 603351, 693154, 791453, 898632, 1015075, 1141166, 1277289, 1423828, 1581167, 1749690, 1929781

Offset: 0

Author

Vincenzo Librandi, Sep 08 2009

Keywords

• nonn
• easy

Comments

For every even n, n^4+(n/2)^3 is a cube.

In effect, a(n) = n*(24*n+3+64*n^2) and 8*a(n)+1 = (8*n+1)^3. [R. J. Mathar, Oct 18 2010]

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A017077.

Programs

Magma

I:=[0, 91, 614, 1953]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Apr 06 2013

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {0, 91, 614, 1953}, 100] (* Vincenzo Librandi, Apr 06 2013 *)

Formula

G.f.: x*(91+250*x+43*x^2)/(1-x)^4. [Colin Barker, Jun 15 2012]

Extensions

Typo corrected by Zak Seidov, Sep 14 2009