OFFSET
0,4
COMMENTS
a(n+1) = largest odd divisor of A000290(n+1). - Jeremy Gardiner, Aug 25 2013
In binary, remove all trailing zeros, then square. - Ralf Stephan, Aug 26 2013
A fractal sequence. The odd-numbered elements give the odd squares A016754. If these elements are removed, the original sequence is recovered. - Jeremy Gardiner, Sep 14 2013
a(n+1) is the denominator of the population variance of the n-th row of Pascal's triangle. - Chai Wah Wu, Mar 25 2018
Multiplicative because A000265 is. - Andrew Howroyd, Jul 26 2018
LINKS
FORMULA
Recurrence: a(2n) = a(n), a(2n+1) = (2n+1)^2. - Ralf Stephan, Aug 26 2013
From Amiram Eldar, Nov 28 2022: (Start)
Multiplicative with a(2^e) = 1, and a(p^e) = p^(2*e) if p > 2.
Sum_{k=1..n} a(k) ~ (4/21) * n^3. (End)
Dirichlet g.f.: zeta(s-2)*(2^s-4)/(2^s-1). - Amiram Eldar, Jan 04 2023
MAPLE
[seq(numer(n^2/2^n), n=0..60)]; # Muniru A Asiru, Mar 31 2018
MATHEMATICA
a[n_] := Numerator[n^2/2^n]; Table[a[n], {n, 0, 200, 2}]
PROG
(PARI) a(n)=(n>>valuation(n, 2))^2 \\ Charles R Greathouse IV & M. F. Hasler, Jun 19 2011
(Python)
from __future__ import division
def A191871(n):
while not n % 2:
n //= 2
return n**2 # Chai Wah Wu, Mar 25 2018
(GAP) List([0..60], n->NumeratorRat(n^2/2^n)); # Muniru A Asiru, Mar 31 2018
CROSSREFS
KEYWORD
nonn,frac,easy,mult
AUTHOR
Vladimir Joseph Stephan Orlovsky, Jun 18 2011
STATUS
approved