A024040 - OEIS

%I #20 Sep 08 2022 08:44:48

%S 1,3,0,-17,0,399,2800,13983,61440,255583,1038576,4179663,16756480,

%T 67080303,268397040,1073691199,4294901760,17179785663,68719371760,

%U 274877776623,1099511467776,4398046316623,17592185810160,70368743897823,281474976378880,1125899906451999

%N a(n) = 4^n - n^4.

%H Vincenzo Librandi, <a href="/A024040/b024040.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (9,-30,50,-45,21,-4).

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

%F E.g.f.: exp(4*x)-(x^4+6*x^3+7*x^2+x)*exp(x). - _Robert Israel_, Dec 29 2014

%p seq(4^n - n^4, n=0..50); # _Robert Israel_, Dec 29 2014

%t lst={}; Do[AppendTo[lst,4^n-n^4],{n,0,5!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 15 2009 *)

%t Table[4^n-n^4,{n,0,40}] (* _Harvey P. Dale_, Nov 10 2019 *)

%o (Magma) [4^n-n^4: n in [0..30]]; // _Vincenzo Librandi_, May 14 2011

%Y Cf. A024012, A024026, A058794. - _Vladimir Joseph Stephan Orlovsky_, Jan 15 2009

%K sign

%O 0,2

%A _N. J. A. Sloane_