A084382 a(n) = n^3 + 6.
6, 7, 14, 33, 70, 131, 222, 349, 518, 735, 1006, 1337, 1734, 2203, 2750, 3381, 4102, 4919, 5838, 6865, 8006, 9267, 10654, 12173, 13830, 15631, 17582, 19689, 21958, 24395, 27006, 29797, 32774, 35943, 39310, 42881, 46662, 50659, 54878, 59325, 64006, 68927, 74094
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Cino Hilliard, Proof that a cube plus 7 cannot be a square.
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Magma
[n^3+6: n in [0..50]]; // Vincenzo Librandi, Jun 10 2016
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Mathematica
Table[n^3 + 6, {n, 0, 60}] (* Vladimir Joseph Stephan Orlovsky, Apr 15 2011 *) LinearRecurrence[{4, -6, 4, -1}, {6, 7, 14, 33}, 60] (* Harvey P. Dale, Aug 08 2013 *) -
PARI
a(n) = n^3 + 6;
Formula
a(0)=6, a(1)=7, a(2)=14, a(3)=33; for n >= 4, a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Harvey P. Dale, Aug 08 2013
G.f.: (6 - 17*x + 22*x^2 - 5*x^3)/(1 - x)^4. - Vincenzo Librandi, Jun 10 2016
E.g.f.: (6 + x + 3*x^2 + x^3)*exp(x). - Elmo R. Oliveira, Apr 20 2025
Extensions
Offset 0 and a(0) = 6 from Vincenzo Librandi, Jun 10 2016