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A082392 Expansion of (1/x) * sum(k>=0, x^2^k/(1-2x^2^(k+1))). 3
1, 1, 2, 1, 4, 2, 8, 1, 16, 4, 32, 2, 64, 8, 128, 1, 256, 16, 512, 4, 1024, 32, 2048, 2, 4096, 64, 8192, 8, 16384, 128, 32768, 1, 65536, 256, 131072, 16, 262144, 512, 524288, 4, 1048576, 1024, 2097152, 32, 4194304, 2048, 8388608, 2, 16777216 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..48.

R. Stephan, Some divide-and-conquer sequences ...

R. Stephan, Table of generating functions

FORMULA

a(0) = 1, a(2*n) = 2^n, a(2*n+1) = a(n).

a(n) = 2^A025480(n) = 2^(A003602(n)-1).

a((2*n+1)*2^p-1) = 2^n, p >= 0 and n >= 0. - Johannes W. Meijer, Feb 11 2013

MAPLE

nmax := 48: for p from 0 to ceil(simplify(log[2](nmax))) do for n from 0 to ceil(nmax/(p+2))+1 do a((2*n+1)*2^p-1) := 2^n od: od: seq(a(n), n=0..nmax); # Johannes W. Meijer, Feb 11 2013

PROG

(PARI) for(n=0, 50, l=ceil(log(n+1)/log(2)); t=polcoeff(sum(k=0, l, (x^2^k)/(1-2*x^2^(k+1)))/x + O(x^(n+1)), n); print1(t", "); ) ;

CROSSREFS

Cf. A045654, A220466.

Sequence in context: A304587 A113418 A117000 * A233327 A085086 A274623

Adjacent sequences:  A082389 A082390 A082391 * A082393 A082394 A082395

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan, Jun 07 2003

STATUS

approved

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Last modified October 21 10:57 EDT 2018. Contains 316414 sequences. (Running on oeis4.)