A112033 a(n) = 3 * 2^(floor(n/2) + 1 + (-1)^n).

12, 3, 24, 6, 48, 12, 96, 24, 192, 48, 384, 96, 768, 192, 1536, 384, 3072, 768, 6144, 1536, 12288, 3072, 24576, 6144, 49152, 12288, 98304, 24576, 196608, 49152, 393216, 98304, 786432, 196608, 1572864, 393216, 3145728, 786432, 6291456, 1572864

Offset: 0

Author

Reinhard Zumkeller, Aug 27 2005

Keywords

• nonn
• easy

References

• George Pólya and Gábor Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part One, Chapter 4, Sect. 1, Problem 148.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..100
• Index entries for linear recurrences with constant coefficients, signature (0,2).

Crossrefs

Cf. A084964, A112030, A112031, A112032.

Programs

Maple

A112033:=n->3*2^(floor(n/2) + 1 + (-1)^n); seq(A112033(k), k=0..50); # Wesley Ivan Hurt, Nov 01 2013

Mathematica

Table[3*2^(Floor[n/2] + 1 + (-1)^n), {n,0,50}] (* Wesley Ivan Hurt, Nov 01 2013 *)

PARI

a(n) = 3 * 2^(n\2 + 1 + (-1)^n); \\ Michel Marcus, Nov 02 2013

Python

def A112033(n): return 3*(1<<(n>>1)+(int(not n&1)<<1)) # Chai Wah Wu, Jan 17 2023

Formula

a(n) = 1 / abs(A112031(n)/A112032(n) - 2/3). (previous name)

a(n) = 3*2^A084964(n) = 3*A112032(n).

From Ralf Stephan, Jul 16 2013: (Start)

Recurrence: a(n) = 2a(n-2), a(0)=12, a(1)=3.

G.f.: (6*x+24)/(1-2*x^2). (End)

From Amiram Eldar, May 11 2025: (Start)

Sum_{n>=0} 1/a(n) = 5/6.

Sum_{n>=0} (-1)^n/a(n) = -1/2. (End)