A132720 - OEIS

%I #20 Sep 23 2024 04:44:56

%S 1,2,4,8,8,16,32,32,64,128,128,256,512,512,1024,2048,2048,4096,8192,

%T 8192,16384,32768,32768,65536,131072,131072,262144,524288,524288,

%U 1048576,2097152,2097152,4194304,8388608,8388608,16777216,33554432,33554432,67108864,134217728,134217728,268435456,536870912,536870912

%N Sequence is identical to its second differences in absolute values.

%H G. C. Greubel, <a href="/A132720/b132720.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,4).

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

%F G.f.: 1 + 2*x*(1 +2*x +4*x^2)/(1 - 4*x^3). - _R. J. Mathar_, Nov 07 2015

%F a(n) = 2^floor((2*n+3)/3) = 2^A004396(n+1), n >= 1. - _G. C. Greubel_, Feb 15 2021 [corrected by _Jason Yuen_, Sep 23 2024]

%F Sum_{n>=0} 1/a(n) = 13/6. - _Amiram Eldar_, Aug 16 2022

%t Join[{1},LinearRecurrence[{0, 0, 4},{2, 4, 8},45]] (* _Ray Chandler_, Sep 23 2015 *)

%t Table[2^Floor[(2*n+3)/3] - Boole[n==0], {n, 0, 45}] (* _G. C. Greubel_, Feb 15 2021 *)

%o (Sage)

%o def A132170(n): return 2^floor((2*n+3)/3) if n>0 else 1

%o [A132170(n) for n in (0..45)] # _G. C. Greubel_, Feb 15 2021

%o (Magma)

%o A132170:= func< n | n eq 0 select 1 else 2^Floor((2*n+3)/3) >;

%o [A132170(n): n in [0..45]]; // _G. C. Greubel_, Feb 15 2021

%Y Cf. A004396.

%K nonn,easy

%O 0,2

%A _Paul Curtz_, Nov 16 2007

%E Terms a(24) onward added by _G. C. Greubel_, Feb 15 2021