A132344 a(n) = n*2^(floor(n/2)).

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

Author

Simon Plouffe, Nov 19 2007

Keywords

• nonn
• easy

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]
• Index entries for linear recurrences with constant coefficients, signature (0,4,0,-4).

Crossrefs

Cf. A004526, A016116.

Programs

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 *)

PARI

a(n) = n*2^(n\2); \\ Michel Marcus, Feb 17 2018

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

Extensions

More terms from Michel Marcus, Feb 17 2018