|
|
A020514
|
|
a(n) = 1^n + 2^n + 4^n + 8^n + 16^n.
|
|
4
|
|
|
5, 31, 341, 4681, 69905, 1082401, 17043521, 270549121, 4311810305, 68853957121, 1100586419201, 17600780175361, 281543712968705, 4504149450301441, 72061992352890881, 1152956690052710401, 18447025552981295105, 295150156996346511361, 4722384497336874434561
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
5th cyclotomic polynomial evaluated at 2^n.
|
|
LINKS
|
|
|
FORMULA
|
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
E.g.f.: exp(x) + exp(2*x) + exp(4*x) + exp(8*x) + exp(16*x). - Philippe Deléham, Apr 06 2013
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
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
|
|
MAPLE
|
with(numtheory, cyclotomic):seq(cyclotomic(5, 2^i), i=0..24);
|
|
MATHEMATICA
|
With[{c=2^Range[0, 4]}, Table[Total[c^n], {n, 0, 20}]] (* Harvey P. Dale, May 27 2012 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|