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A029745 Expansion of (1 + 2x + 6x^2 + x^3)/(1 - 2x^2). 1
1, 2, 8, 5, 16, 10, 32, 20, 64, 40, 128, 80, 256, 160, 512, 320, 1024, 640, 2048, 1280, 4096, 2560, 8192, 5120, 16384, 10240, 32768, 20480, 65536, 40960, 131072, 81920, 262144, 163840, 524288, 327680, 1048576, 655360, 2097152, 1310720, 4194304 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Note that 4 is the only power of 2 not here. All terms are either 2^k or 5*2^k.
LINKS
FORMULA
G.f.: (1 + 2x + 6x^2 + x^3)/(1 - 2x^2).
Sum_{n>=1} 1/a(n) = 43/20. - Amiram Eldar, Jan 21 2022
MATHEMATICA
LinearRecurrence[{0, 2}, {1, 2, 8, 5}, 50] (* or *) With[{nn=20}, Join[{1, 2}, Riffle[ 8*2^Range[0, nn], 5 2^Range[0, nn]]]] (* Harvey P. Dale, Sep 28 2016 *)
PROG
(PARI) a(n)=if(n<2, 1+max(-1, n), 2^(n\2)*if(n%2, 5/2, 4))
CROSSREFS
Cf. A094958 (numbers of the form 2^k or 5*2^k).
Sequence in context: A309792 A318725 A155901 * A332067 A183232 A344691
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Edited by T. D. Noe, Nov 12 2010
STATUS
approved

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Last modified March 29 04:59 EDT 2024. Contains 371264 sequences. (Running on oeis4.)