A175166 a(n) = 64*(2^n - 1).

0, 64, 192, 448, 960, 1984, 4032, 8128, 16320, 32704, 65472, 131008, 262080, 524224, 1048512, 2097088, 4194240, 8388544, 16777152, 33554368, 67108800, 134217664, 268435392, 536870848, 1073741760

Offset: 0

Author

Reinhard Zumkeller, Feb 28 2010

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

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).

Cf. A173787, A175161.

Programs

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

Mathematica

LinearRecurrence[{3,-2},{0,64},30] (* Harvey P. Dale, Apr 08 2015 *)

Python

def A175166(n): return (1<Chai Wah Wu, Jun 27 2023

Sage

[64*(2^n -1) for n in (0..40)] # G. C. Greubel, Jul 08 2021

Formula

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

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

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

a(n) = 3*a(n-1) - 2*a(n-2), a(0)=0, a(1)=64. - Vincenzo Librandi, Dec 28 2010

From G. C. Greubel, Jul 08 2021: (Start)

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

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