

A062510


a(n) = 2^n + (1)^(n+1).


29



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
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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 Engeltype 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:math/0204173 [math.NT], 2002.
Index entries for 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)*(12*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
E.g.f.: (exp(3*x)  1)*exp(x).  Ilya Gutkovskiy, Nov 20 2016


MATHEMATICA

LinearRecurrence[{1, 2}, {0, 3}, 30] (* or *) Table[2^n  (1)^n, {n, 0, 30}] (* G. C. Greubel, Jan 15 2018 *)


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 A285883
Adjacent sequences: A062507 A062508 A062509 * A062511 A062512 A062513


KEYWORD

easy,nonn


AUTHOR

Jason Earls, Jun 24 2001


EXTENSIONS

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


STATUS

approved



