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A062510 a(n) = 2^n + (-1)^(n+1). 35
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
G. Everest, Y. Puri and T. Ward, Integer sequences counting periodic points, arXiv:math/0204173 [math.NT], 2002.
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
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
Sequence in context: A233026 A105423 A147471 * A000200 A100744 A331519
KEYWORD
easy,nonn
AUTHOR
Jason Earls, Jun 24 2001
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Jul 06 2001
STATUS
approved

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Last modified June 17 15:57 EDT 2024. Contains 373463 sequences. (Running on oeis4.)