A175164 a(n) = 16*(2^n - 1).

0, 16, 48, 112, 240, 496, 1008, 2032, 4080, 8176, 16368, 32752, 65520, 131056, 262128, 524272, 1048560, 2097136, 4194288, 8388592, 16777200, 33554416, 67108848, 134217712, 268435440

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), this sequence (m=16), A175165 (m=32), A175166 (m=64).

Cf. A140504, A173787.

Programs

Magma

I:=[0,16]; [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

16*(2^Range[0,40] - 1) (* G. C. Greubel, Jul 08 2021 *)

Python

def A175164(n): return (1<Chai Wah Wu, Jun 27 2023

Sage

[16*(2^n -1) for n in (0..40)] # G. C. Greubel, Jul 08 2021

Formula

a(n) = 2^(n+4) - 16.

a(n) = A173787(n+4, 4).

a(2*n) = A140504(n+2)*A028399(n).

a(n) = 3*a(n-1) - 2*a(n-2), a(0)=0, a(1)=16. - Vincenzo Librandi, Dec 28 2010

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

G.f.: 16*x/((1-x)*(1-2*x)).

E.g.f.: 16*(exp(2*x) - exp(x)). (End)