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URL: https://oeis.org/A186035

⇱ A186035 - OEIS

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A186035
a(n) = (-1)^A186034(n).
3
1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1
OFFSET
0
COMMENTS
Hankel transform is A186036.
LINKS
FORMULA
a(n) = (-1)^log_2(A001006(n)/numerator(A001006(n)/2^n)).
a(n) = (-1)^A007814(A001006(n)). - Antti Karttunen, Aug 12 2017
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2/3. - Amiram Eldar, Aug 26 2024
PROG
(Python)
from itertools import count, islice
def A186035_gen(): # generator of terms
a, b = 1, 1
yield from (1, 1)
for n in count(2):
a, b = b, (b*(2*n+1)+a*3*(n-1))//(n+2)
yield 1-(((~b&b-1).bit_length()&1)<<1)
A186035_list = list(islice(A186035_gen(), 30)) # Chai Wah Wu, Jul 08 2022
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Paul Barry, Feb 11 2011
EXTENSIONS
More terms from Antti Karttunen, Aug 12 2017
STATUS
approved