cp's OEIS Frontend

A020514 a(n) = 1^n + 2^n + 4^n + 8^n + 16^n.

%I A020514 #44 Dec 07 2019 12:18:20
%S A020514 5,31,341,4681,69905,1082401,17043521,270549121,4311810305,
%T A020514 68853957121,1100586419201,17600780175361,281543712968705,
%U A020514 4504149450301441,72061992352890881,1152956690052710401,18447025552981295105,295150156996346511361,4722384497336874434561
%N A020514 a(n) = 1^n + 2^n + 4^n + 8^n + 16^n.
%C A020514 5th cyclotomic polynomial evaluated at 2^n.
%H A020514 T. D. Noe, <a href="/A020514/b020514.txt">Table of n, a(n) for n = 0..200</a>
%H A020514 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (31,-310,1240,-1984,1024).
%F A020514 G.f.: 1/(1-x)+1/(1-2*x)+1/(1-4*x)+1/(1-8*x)+1/(1-16*x). - _Philippe Deléham_, Apr 06 2013
%F A020514 E.g.f.: exp(x) + exp(2*x) + exp(4*x) + exp(8*x) + exp(16*x). - _Philippe Deléham_, Apr 06 2013
%F A020514 a(n) = 31*a(n-1) - 310*a(n-2) + 1240*a(n-3) - 1984*a(n-4) + 1024*a(n-5) with a(0) = 5, a(1) = 31, a(2) = 341, a(3) = 4681, a(4) = 69905. - _Philippe Deléham_, Apr 06 2013
%F A020514 a(n) = (2^(5*n) - 1)/( 2^n - 1). Exp( Sum_{n >= 1} a(n)*x^n/n ) = 1 + 31*x + 651*x^2 + 11811*x^3 + ... is the o.g.f. for the 4th subdiagonal of triangle A022166, essentially A006097. - _Peter Bala_, Apr 07 2015
%p A020514 with(numtheory,cyclotomic):seq(cyclotomic(5,2^i),i=0..24);
%t A020514 With[{c=2^Range[0,4]},Table[Total[c^n],{n,0,20}]] (* _Harvey P. Dale_, May 27 2012 *)
%o A020514 (Sage) [sigma(16,n)for n in range(0,16)] # _Zerinvary Lajos_, Jun 04 2009
%o A020514 (PARI) a(n)=1^n+2^n+4^n+8^n+16^n \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A020514 Cf. A082771, A006097, A022166.
%K A020514 nonn,easy
%O A020514 0,1
%A A020514 _Simon Plouffe_ and _N. J. A. Sloane_