A175162 a(n) = 16*(2^n + 1).

32, 48, 80, 144, 272, 528, 1040, 2064, 4112, 8208, 16400, 32784, 65552, 131088, 262160, 524304, 1048592, 2097168, 4194320, 8388624, 16777232, 33554448, 67108880, 134217744, 268435472, 536870928, 1073741840, 2147483664, 4294967312, 8589934608, 17179869200

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), A175161 (m=8), this sequence (m=16), A175163 (m=32).

Cf. A173786.

Programs

Magma

I:=[32,48]; [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[0,30] +1) (* or *) LinearRecurrence[{3,-2},{32,48},30] (* Harvey P. Dale, Jun 08 2017 *)

Sage

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

Formula

a(n) = A173786(n+4, 4).

a(n) = 3*a(n-1) - 2*a(n-2), a(0)=32, a(1)=48. - Vincenzo Librandi, Dec 28 2010

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

G.f.: 16*(2 - 3*x)/((1-x)*(1-2*x)).

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