OFFSET
0,1
COMMENTS
5th cyclotomic polynomial evaluated at 2^n.
LINKS
T. D. Noe, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (31,-310,1240,-1984,1024).
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
(Sage) [sigma(16, n)for n in range(0, 16)] # Zerinvary Lajos, Jun 04 2009
(PARI) a(n)=1^n+2^n+4^n+8^n+16^n \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved