A130508 a(1)=2. a(2)=3. a(3)=1. a(n+3) = 3 + a(n), for all positive integers n.
2, 3, 1, 5, 6, 4, 8, 9, 7, 11, 12, 10, 14, 15, 13, 17, 18, 16, 20, 21, 19, 23, 24, 22, 26, 27, 25, 29, 30, 28, 32, 33, 31, 35, 36, 34, 38, 39, 37, 41, 42, 40, 44, 45, 43, 47, 48, 46, 50, 51, 49, 53, 54, 52, 56, 57, 55, 59, 60, 58, 62, 63, 61, 65, 66, 64, 68
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
Crossrefs
Cf. A130509.
Programs
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Mathematica
Transpose[NestList[{#[[2]],#[[3]],#[[1]]+3}&,{2,3,1},100]][[1]] (* Harvey P. Dale, Sep 08 2011 *) LinearRecurrence[{1,0,1,-1},{2,3,1,5},100] (* Harvey P. Dale, Feb 02 2015 *)
Formula
a(1)=2, a(2)=3, a(3)=1, a(4)=5, a(n)=a(n-1)+a(n-3)-a(n-4). - Harvey P. Dale, Feb 02 2015
a(n) = n - 2*cos(2*n*Pi/3). - Wesley Ivan Hurt, Sep 27 2017
G.f.: x*(2+x-2*x^2+2*x^3) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 03 2021
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*Pi/(3*sqrt(3)) - log(2)/3. - Amiram Eldar, Jan 31 2023
Comments