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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, 3145726, 3145727, 6291454 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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) = A081026(n+1)-1.
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
E.g.f.: (3*cosh(sqrt(2)*x) - 4*sinh(x) + 3*sqrt(2)*sinh(sqrt(2)*x) - 2*cosh(x) - 1)/2. - Stefano Spezia, Jul 11 2023
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
Sequence in context: A365501 A080735 A091856 * A022770 A141481 A241268
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 February 20 21:52 EST 2024. Contains 370219 sequences. (Running on oeis4.)