A175166 - OEIS

%I #31 May 16 2026 23:03:44

%S 0,64,192,448,960,1984,4032,8128,16320,32704,65472,131008,262080,

%T 524224,1048512,2097088,4194240,8388544,16777152,33554368,67108800,

%U 134217664,268435392,536870848,1073741760,2147483584,4294967232,8589934528,17179869120,34359738304

%N a(n) = 64*(2^n - 1).

%H G. C. Greubel, <a href="/A175166/b175166.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).

%F a(n) = 2^(n+6) - 64.

%F a(n) = A173787(n+6, 6).

%F a(2*n) = A175161(n)*A159741(n) for n > 0.

%F a(n) = 3*a(n-1) - 2*a(n-2), a(0)=0, a(1)=64. - _Vincenzo Librandi_, Dec 28 2010

%F From _G. C. Greubel_, Jul 08 2021: (Start)

%F G.f.: 64*x/((1-x)*(1-2*x)).

%F E.g.f.: 64*(exp(2*x) - exp(x)). (End)

%t LinearRecurrence[{3,-2},{0,64},30] (* _Harvey P. Dale_, Apr 08 2015 *)

%o (Magma) I:=[0,64]; [n le 2 select I[n] else 3*Self(n-1) - 2*Self(n-2): n in [1..41]]; // _G. C. Greubel_, Jul 08 2021

%o (SageMath) [64*(2^n -1) for n in (0..40)] # _G. C. Greubel_, Jul 08 2021

%o (Python)

%o def A175166(n): return (1<<n)-1<<6 # _Chai Wah Wu_, Jun 27 2023

%o (PARI) a(n)=64*(2^n-1) \\ _Charles R Greathouse IV_, May 16 2026

%Y Sequences of the form m*(2^n - 1): A000225 (m=1), A000918 (m=2), A068156 (m=3), A028399 (m=4), A068293 (m=6), A159741 (m=8), A175164 (m=16), A175165 (m=32), this sequence (m=64).

%Y Cf. A173787, A175161.

%K nonn,easy

%O 0,2

%A _Reinhard Zumkeller_, Feb 28 2010