A024040 a(n) = 4^n - n^4.

1, 3, 0, -17, 0, 399, 2800, 13983, 61440, 255583, 1038576, 4179663, 16756480, 67080303, 268397040, 1073691199, 4294901760, 17179785663, 68719371760, 274877776623, 1099511467776, 4398046316623, 17592185810160, 70368743897823, 281474976378880, 1125899906451999

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (9,-30,50,-45,21,-4).

Crossrefs

Cf. A024012, A024026, A058794. - Vladimir Joseph Stephan Orlovsky, Jan 15 2009

Programs

Magma

[4^n-n^4: n in [0..30]]; // Vincenzo Librandi, May 14 2011

Maple

seq(4^n - n^4, n=0..50); # Robert Israel, Dec 29 2014

Mathematica

lst={}; Do[AppendTo[lst,4^n-n^4],{n,0,5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 15 2009 *)
Table[4^n-n^4,{n,0,40}] (* Harvey P. Dale, Nov 10 2019 *)

Formula

G.f.: (1-6*x+3*x^2+23*x^3+48*x^4+3*x^5)/((1-4*x)*(1-x)^5).

E.g.f.: exp(4*x)-(x^4+6*x^3+7*x^2+x)*exp(x). - Robert Israel, Dec 29 2014