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A132344
a(n) = n*2^(floor(n/2)).
1
0, 1, 4, 6, 16, 20, 48, 56, 128, 144, 320, 352, 768, 832, 1792, 1920, 4096, 4352, 9216, 9728, 20480, 21504, 45056, 47104, 98304, 102400, 212992, 221184, 458752, 475136, 983040, 1015808, 2097152, 2162688, 4456448, 4587520, 9437184, 9699328, 19922944, 20447232, 41943040, 42991616
OFFSET
0,3
COMMENTS
This sequence is related to a greedily and recursively defined sequence (see links). - Sela Fried, Aug 30 2024
LINKS
Sela Fried, On integer sequence A128135, 2024.
Sela Fried, Proofs of some Conjectures from the OEIS, arXiv:2410.07237 [math.NT], 2024. See p. 11.
Simon Plouffe, Illustration. [broken link]
FORMULA
G.f.: x*(1 + 4*x + 2*x^2)/(1 - 2*x^2)^2. - Ilya Gutkovskiy, Feb 24 2017
a(n) = n*A016116(n). - Michel Marcus, Feb 17 2018
Sum{n>=1} 1/a(n) = sqrt(2)*arcsinh(1) + log(2)/2. - Amiram Eldar, Sep 15 2024
MAPLE
seq(n*2^(floor(n/2)), n=1..120);
MATHEMATICA
Table[n*2^Floor[n/2], {n, 0, 100}] (* Wesley Ivan Hurt, Dec 12 2013 *)
LinearRecurrence[{0, 4, 0, -4}, {0, 1, 4, 6}, 50] (* Harvey P. Dale, Aug 27 2022 *)
PROG
(PARI) a(n) = n*2^(n\2); \\ Michel Marcus, Feb 17 2018
CROSSREFS
Sequence in context: A304909 A302119 A120542 * A306905 A097970 A044858
KEYWORD
nonn,easy
AUTHOR
Simon Plouffe, Nov 19 2007
EXTENSIONS
More terms from Michel Marcus, Feb 17 2018
STATUS
approved