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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 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)*(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 Cf. A102345, A105723. Sequence in context: A233026 A105423 A147471 * A000200 A100744 A331519 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

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