A084964 Follow n+2 by n. Also solution of a(n+2)=a(n)+1, a(0)=2, a(1)=0.
2, 0, 3, 1, 4, 2, 5, 3, 6, 4, 7, 5, 8, 6, 9, 7, 10, 8, 11, 9, 12, 10, 13, 11, 14, 12, 15, 13, 16, 14, 17, 15, 18, 16, 19, 17, 20, 18, 21, 19, 22, 20, 23, 21, 24, 22, 25, 23, 26, 24, 27, 25, 28, 26, 29, 27, 30, 28, 31, 29, 32, 30, 33, 31, 34, 32, 35, 33, 36, 34, 37, 35, 38, 36, 39
Offset: 0
Links
- Stefano Spezia, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
- Index entries for two-way infinite sequences
Programs
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Haskell
import Data.List (transpose) a084964 n = a084964_list !! n a084964_list = concat $ transpose [[2..], [0..]] -- Reinhard Zumkeller, Apr 06 2015
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Magma
&cat[ [n+2, n]: n in [0..37] ]; // Klaus Brockhaus, Nov 23 2009
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Maple
A084964:=n->floor(n/2)+1+(-1)^n; seq(A084964(k), k=0..100); # Wesley Ivan Hurt, Nov 08 2013
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Mathematica
lst={}; a=1; Do[a=n-a; AppendTo[lst, a], {n, 0, 100}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 14 2008 *) Table[{n,n-2},{n,2,40}]//Flatten (* or *) LinearRecurrence[{1,1,-1},{2,0,3},80] (* Harvey P. Dale, Sep 12 2021 *) -
PARI
a(n)=n\2-2*(n%2)+2
Formula
G.f.: (2-2x+x^2)/((1-x)(1-x^2)).
a(2n+1)=n. a(2n)=n+2. a(n+2)=a(n)+1. a(n)=-a(-3-n).
a(n) = floor(n/2) + 1 + (-1)^n. - Reinhard Zumkeller, Aug 27 2005
A112032(n)=2^a(n); A112033(n)=3*2^a(n); a(n)=A109613(n+2)-A052938(n). - Reinhard Zumkeller, Aug 27 2005
a(n) = n + 1 - a(n-1) (with a(0)=2). - Vincenzo Librandi, Aug 08 2010
a(n) = floor(n/2)*3 - floor((n-1)/2)*2. - Ross La Haye, Mar 27 2013
a(n) = 3*n - 3 - 5*floor((n-1)/2). - Wesley Ivan Hurt, Nov 08 2013
a(n) = (3 + 5*(-1)^n + 2*n)/4. - Wolfgang Hintze, Dec 13 2014
E.g.f.: ((4 + x)*cosh(x) - (1 - x)*sinh(x))/2. - Stefano Spezia, Jul 01 2023
Extensions
First part of definition adjusted to match offset by Klaus Brockhaus, Nov 23 2009