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A191871
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a(n) = numerator(n^2 / 2^n).
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6
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0, 1, 1, 9, 1, 25, 9, 49, 1, 81, 25, 121, 9, 169, 49, 225, 1, 289, 81, 361, 25, 441, 121, 529, 9, 625, 169, 729, 49, 841, 225, 961, 1, 1089, 289, 1225, 81, 1369, 361, 1521, 25, 1681, 441, 1849, 121, 2025, 529, 2209, 9, 2401, 625, 2601, 169, 2809, 729, 3025
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listen;
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OFFSET
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0,4
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COMMENTS
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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
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LINKS
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FORMULA
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Recurrence: a(2n) = a(n), a(2n+1) = (2n+1)^2. - Ralf Stephan, Aug 26 2013
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
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MAPLE
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MATHEMATICA
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a[n_] := Numerator[n^2/2^n]; Table[a[n], {n, 0, 200, 2}]
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PROG
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(Python)
from __future__ import division
while not n % 2:
n //= 2
(GAP) List([0..60], n->NumeratorRat(n^2/2^n)); # Muniru A Asiru, Mar 31 2018
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CROSSREFS
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KEYWORD
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nonn,frac,easy,mult
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AUTHOR
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STATUS
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approved
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