A132720 Sequence is identical to its second differences in absolute values.

1, 2, 4, 8, 8, 16, 32, 32, 64, 128, 128, 256, 512, 512, 1024, 2048, 2048, 4096, 8192, 8192, 16384, 32768, 32768, 65536, 131072, 131072, 262144, 524288, 524288, 1048576, 2097152, 2097152, 4194304, 8388608, 8388608, 16777216, 33554432, 33554432, 67108864, 134217728, 134217728, 268435456, 536870912, 536870912

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

After 1, 2, repeat 4^p, 2*4^p, 2*4^p, p positive.

G.f.: 1 + 2*x*(1 +2*x +4*x^2)/(1 - 4*x^3). - R. J. Mathar, Nov 07 2015

From G. C. Greubel, Feb 15 2021: (Start)

a(2*n+1) = 2^floor((4*n+1)/3) = 2^A042965(n+1).

a(2*n) = 2^floor((2*n+3)/3)) = 2^A042968(n), n >= 1. (End)

Sum_{n>=0} 1/a(n) = 13/6. - Amiram Eldar, Aug 16 2022

Mathematica

Join[{1}, LinearRecurrence[{0, 0, 4}, {2, 4, 8}, 45]] (* Ray Chandler, Sep 23 2015 *)
Table[If[EvenQ[n], 2^Floor[(2*n+3)/3] - Boole[n==0], 2^Floor[(2*n+3)/3]], {n, 0, 45}] (* G. C. Greubel, Feb 15 2021 *)

Prog

(Sage)
def A132170(n): return 2^floor((2*n+3)/3) if n%2==0 else 2^floor((2*n+3)/3)
[1]+[A132170(n) for n in (1..45)] # G. C. Greubel, Feb 15 2021
(Magma)
A132170:= func< n | n eq 0 select 1 else (n mod 2 eq 0) select 2^Floor((2*n+3)/3) else 2^Floor((2*n+3)/3) >;
[A132170(n): n in [0..45]]; // G. C. Greubel, Feb 15 2021

Crossrefs

Cf. A042965, A042968.

Sequence in context: A073616 A076735 A192097 * A029930 A334284 A193850

Adjacent sequences: A132717 A132718 A132719 * A132721 A132722 A132723

Keyword

nonn,easy

Author

Paul Curtz, Nov 16 2007

Extensions

Terms a(24) onward added by G. C. Greubel, Feb 15 2021

Status

approved