A013730 a(n) = 2^(3*n+1).

2, 16, 128, 1024, 8192, 65536, 524288, 4194304, 33554432, 268435456, 2147483648, 17179869184, 137438953472, 1099511627776, 8796093022208, 70368744177664, 562949953421312, 4503599627370496, 36028797018963968, 288230376151711744, 2305843009213693952, 18446744073709551616

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

1/2 + 1/16 + 1/128 + 1/1024 + ... = 4/7. - Gary W. Adamson, Aug 29 2008

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Tanya Khovanova, Recursive Sequences.
• Index entries for linear recurrences with constant coefficients, signature (8).
• Index to divisibility sequences.

Crossrefs

Cf. A013731, A016921, A016933, A132024, A157176.

Programs

Magma

[2^(3*n+1): n in [0..30]]; // Vincenzo Librandi, May 04 2011

Maple

seq(2^(3*n+1),n=0..19); # Nathaniel Johnston, Jun 26 2011

Mathematica

Table[2^n, {n, 1, 100, 3}] (* Vladimir Joseph Stephan Orlovsky, Jun 14 2011 *)
2^(3 Range[0, 40] + 1) (* Vladimir Joseph Stephan Orlovsky, Jun 14 2011 *)
Table[2^(3 n + 1), {n, 0, 20}] (* Eric W. Weisstein, Nov 03 2024 *)
2^(3 Range[0, 20] + 1) (* Eric W. Weisstein, Nov 03 2024 *)
2^Range[1, 61, 3] (* Eric W. Weisstein, Nov 03 2024 *)
LinearRecurrence[{8}, {2}, 20] (* Eric W. Weisstein, Nov 03 2024 *)
CoefficientList[Series[2/(1 - 8 x), {x, 0, 20}], x] (* Eric W. Weisstein, Nov 03 2024 *)

PARI

a(n)=2<<(3*n) \\ Charles R Greathouse IV, Jun 14 2011

Formula

From Philippe Deléham, Nov 23 2008: (Start)

a(n) = 8*a(n-1), n > 0; a(0)=2.

G.f.: 2/(1-8x). (End)

a(n) = A157176(A016921(n)) = A157176(A016933(n)). - Reinhard Zumkeller, Feb 24 2009

From Amiram Eldar, May 08 2023: (Start)

Sum_{n>=0} (-1)^n/a(n) = 4/9.

Product_{n>=0} (1 - 1/a(n)) = A132024. (End)

E.g.f.: 2*exp(8*x). - Stefano Spezia, May 29 2024