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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
OFFSET
1,2
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) = 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
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