login
This site is supported by donations to The OEIS Foundation.

 

Logo

Many excellent designs for a new banner were submitted. We will use the best of them in rotation.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A062510 2^n + (-1)^(n+1). 21
0, 3, 3, 9, 15, 33, 63, 129, 255, 513, 1023, 2049, 4095, 8193, 16383, 32769, 65535, 131073, 262143, 524289, 1048575, 2097153, 4194303, 8388609, 16777215, 33554433, 67108863, 134217729, 268435455, 536870913, 1073741823, 2147483649 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The identity 2 = 2^2/3 + 2^3/(3*3) - 2^4/(3*3*9) - 2^5/(3*3*9*15) + + - - can be viewed as a generalized Engel-type expansion of the number 2 to the base 2. Compare with A014551. - Peter Bala, Nov 13 2013

REFERENCES

D. M. Burton, Elementary Number Theory, Allyn and Bacon, Inc. Boston, MA, 1976, p. 29.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

G. Everest, Y. Puri and T. Ward, Integer sequences counting periodic points, arXiv:0204173

Index to sequences with linear recurrences with constant coefficients, signature (1,2).

FORMULA

a(n) = 3*A001045(n). - Paul Curtz, Jan 17 2008

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

G.f.: Q(0) where Q(k)= 1 - 1/(4^k - 2*x*16^k/(2*x*4^k - 1/(1 + 1/(2*4^k - 8*x*16^k/(4*x*4^k + 1/Q(k+1) ))))); (continued fraction). - Sergei N. Gladkovskii, Apr 13 2013

PROG

(PARI) for(n=0, 22, print(2^n+(-1)^(n+1)))

(MAGMA) [2^n + (-1)^(n+1): n in [0..40]]; // Vincenzo Librandi, Aug 14 2011

CROSSREFS

Cf. A102345, A105723.

Sequence in context: A233026 A105423 A147471 * A000200 A100744 A232948

Adjacent sequences:  A062507 A062508 A062509 * A062511 A062512 A062513

KEYWORD

easy,nonn

AUTHOR

Jason Earls (zevi_35711(AT)yahoo.com), Jun 24 2001

EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), Jul 06 2001

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified April 20 13:52 EDT 2014. Contains 240806 sequences.