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a(n) = n^3 + 6.
2

%I #26 Sep 08 2022 08:45:11

%S 6,7,14,33,70,131,222,349,518,735,1006,1337,1734,2203,2750,3381,4102,

%T 4919,5838,6865,8006,9267,10654,12173,13830,15631,17582,19689,21958,

%U 24395,27006,29797,32774,35943,39310,42881,46662,50659,54878,59325,64006

%N a(n) = n^3 + 6.

%H Vincenzo Librandi, <a href="/A084382/b084382.txt">Table of n, a(n) for n = 0..1000</a>

%H Cino Hilliard, <a href="https://web.archive.org/web/20080621104333/http://groups.msn.com:80/BC2LCC/n37ltk2.msnw">Proof that a cube plus 7 cannot be a square</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F a(1)=7, a(2)=14, a(3)=33, a(4)=70; 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

%F G.f.: (6 - 17*x + 22*x^2 - 5*x^3)/(1 - x)^4. - _Vincenzo Librandi_, Jun 10 2016

%t Table[n^3 + 6, {n, 0, 60}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 15 2011 *)

%t LinearRecurrence[{4, -6, 4, -1}, {6, 7, 14, 33}, 60] (* _Harvey P. Dale_, Aug 08 2013 *)

%o (PARI) a(n) = n^3 + 6;

%o (Magma) [n^3+6: n in [0..50]]; // _Vincenzo Librandi_, Jun 10 2016

%Y Cf. A000578, A084378, A084381.

%K nonn,easy

%O 0,1

%A _Cino Hilliard_, Jun 23 2003

%E Offset 0 and a(0) = 6 from _Vincenzo Librandi_, Jun 10 2016