A140504 a(n) = 2^n + 4.

5, 6, 8, 12, 20, 36, 68, 132, 260, 516, 1028, 2052, 4100, 8196, 16388, 32772, 65540, 131076, 262148, 524292, 1048580, 2097156, 4194308, 8388612, 16777220, 33554436, 67108868, 134217732, 268435460, 536870916, 1073741828

Offset: 0

Author

Paul Curtz, Jun 30 2008

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

Cf. A000051 (m=0), A052548 (m=2), this sequence (m=4), A153973 (m=6), A231643 (m=5), A175161 (m=8), A175162 (m=16), A175163 (m=32).

Programs

Magma

[2^n +4: n in [0..30]]; // G. C. Greubel, Jul 08 2021

Mathematica

Table[2^n + 4, {n, 0, 30}] (* Stefan Steinerberger, Aug 04 2008 *)
LinearRecurrence[{3,-2}, {5,6}, 40] (* Harvey P. Dale, May 26 2018 *)

PARI

a(n)=2^n+4 \\ Charles R Greathouse IV, Dec 21 2011

Sage

[2^n + 4 for n in range(0,31)] # Zerinvary Lajos, May 31 2009

Formula

G.f.: (5 - 9*x)/((1 - x)*(1 - 2*x)). - Jaume Oliver Lafont, Aug 30 2009

a(n) = 2*a(n-1) - 4 with a(0) = 5. - Vincenzo Librandi, Nov 24 2009

From Reinhard Zumkeller, Feb 28 2010: (Start)

a(n) = A173786(n,2) for n > 1.

a(n+2)*A028399(n) = A175164(2*n). (End)

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

a(n) = m*(2^(n-2) + 1), with m = 4.

E.g.f.: exp(2*x) + 4*exp(x). (End)

Extensions

More terms from Stefan Steinerberger, Aug 04 2008