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 A083416 Add 1, double, add 1, double, etc. 7
 1, 2, 4, 5, 10, 11, 22, 23, 46, 47, 94, 95, 190, 191, 382, 383, 766, 767, 1534, 1535, 3070, 3071, 6142, 6143, 12286, 12287, 24574, 24575, 49150, 49151, 98302, 98303, 196606, 196607, 393214, 393215, 786430, 786431, 1572862, 1572863 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..5000 Index entries for linear recurrences with constant coefficients, signature (0,3,0,-2). FORMULA G.f.: x*(1+2*x+x^2-x^3)/(1-x^2)/(1-2*x^2). a(2*n) = 3*2^(n-1)-1, a(2*n+1) = 3*2^n-2. a(n) = 3*2^((2*n-(-1)^n-3)/4)+((-1)^n-3)/2. - Bruno Berselli, Feb 17 2011 For n > 1: a(n) = (1 + n mod 2) * a(n-1) + 1 - n mod 2. - Reinhard Zumkeller, Feb 27 2012 a(2n+1) = A033484(n), a(2n) = A153893(n). - Philippe Deléham, Apr 14 2013 MAPLE A083416 := proc(n) if type(n, 'even') then 3*2^(n/2-1)-1 ; else 3*2^((n-1)/2)-2 ; end if; end proc: # R. J. Mathar, Feb 16 2011 MATHEMATICA a=0; b=0; lst={a, b}; Do[z=a+b+1; AppendTo[lst, z]; a=b; b=z; z=b+1; AppendTo[lst, z]; a=b; b=z, {n, 50}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 16 2010 *) LinearRecurrence[{0, 3, 0, -2}, {1, 2, 4, 5}, 40] (* Harvey P. Dale, Nov 18 2014 *) PROG (MAGMA) [Floor(3*2^((2*n-(-1)^n-3)/4)+((-1)^n-3)/2): n in [1..50]]; // Vincenzo Librandi, Aug 17 2011 (Haskell) a083416 n = a083416_list !! (n-1) a083416_list = 1 : f 2 1 where    f x y = z : f (x+1) z where z = (1 + x `mod` 2) * y + 1 - x `mod` 2 -- Reinhard Zumkeller, Feb 27 2012 CROSSREFS a(n) = A081026(n+1)-1. Cf. A075427. - Robert Ferreol, Feb 16 2011 Sequence in context: A299322 A080735 A091856 * A022770 A141481 A241268 Adjacent sequences:  A083413 A083414 A083415 * A083417 A083418 A083419 KEYWORD easy,nonn AUTHOR N. J. A. Sloane, Jun 10 2003 EXTENSIONS More terms from Donald Sampson (marsquo(AT)hotmail.com), Dec 04 2003 Corrected by T. D. Noe, Nov 02 2006 STATUS approved

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Last modified October 14 07:19 EDT 2019. Contains 327995 sequences. (Running on oeis4.)