A175161 a(n) = 8*(2^n + 1).

16, 24, 40, 72, 136, 264, 520, 1032, 2056, 4104, 8200, 16392, 32776, 65544, 131080, 262152, 524296, 1048584, 2097160, 4194312, 8388616, 16777224, 33554440, 67108872, 134217736, 268435464, 536870920, 1073741832, 2147483656, 4294967304, 8589934600, 17179869192

Offset: 0

Author

Reinhard Zumkeller, Feb 28 2010

Keywords

• nonn
• easy

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): A000051 (m=1), A052548 (m=2), A140504 (m=4), A153973 (m=6), A231643 (m=5), this sequence (m=8), A175162 (m=16), A175163 (m=32).

Cf. A159741, A173786, A175166.

Programs

Magma

I:=[16,24]; [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

8*(2^Range[0, 40] + 1) (* G. C. Greubel, Jul 08 2021 *)
LinearRecurrence[{3,-2},{16,24},40] (* Harvey P. Dale, Feb 10 2022 *)

Sage

[8*(2^n +1) for n in (0..40)] # G. C. Greubel, Jul 08 2021

Formula

a(n) = A173786(n+3, 3).

a(n) = A175166(2*n)/A159741(n) for n > 0.

a(n) = 3*a(n-1) -2*a(n-2) with a(0)=16, a(1)=24. - Vincenzo Librandi, Dec 28 2010

G.f.: 8*(2 - 3*x)/((1-x)*(1-2*x)). - Chai Wah Wu, Jun 20 2020

a(n) = 8 * A000051(n). - Alois P. Heinz, Jun 20 2020

E.g.f.: 8*(exp(2*x) + exp(x)). - G. C. Greubel, Jul 08 2021