A175165 a(n) = 32*(2^n - 1).

0, 32, 96, 224, 480, 992, 2016, 4064, 8160, 16352, 32736, 65504, 131040, 262112, 524256, 1048544, 2097120, 4194272, 8388576, 16777184, 33554400, 67108832, 134217696, 268435424, 536870880

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), this sequence (m=32), A175166 (m=64).

Cf. A173787.

Programs

Magma

I:=[0,32]; [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

32(2^Range[0,30] -1) (* or *) LinearRecurrence[{3,-2},{0,32},30] (* Harvey P. Dale, Mar 23 2015 *)

Python

def A175165(n): return (1<Chai Wah Wu, Jun 27 2023

Sage

[32*(2^n -1) for n in (0..40)] # G. C. Greubel, Jul 08 2021

Formula

a(n) = 2^(n+5) - 32.

a(n) = A173787(n+5, 5).

a(n) = 3*a(n-1) - 2*a(n-2); a(0)=0, a(1)=32. - Vincenzo Librandi, Dec 28 2010

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

G.f.: 32*x/((1-x)*(1-2*x)).

E.g.f.: 32*(exp(2*x) - exp(x)). (End)