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A174562 a(1)=2, a(2)=3, then a(n)=a(n-1)+a(n-2) if n odd, a(n)=a(n-1)-a(n-2) if n even. 2
2, 3, 5, 2, 7, 5, 12, 7, 19, 12, 31, 19, 50, 31, 81, 50, 131, 81, 212, 131, 343, 212, 555, 343, 898, 555, 1453, 898, 2351, 1453, 3804, 2351, 6155, 3804, 9959, 6155, 16114, 9959, 26073, 16114, 42187, 26073, 68260, 42187, 110447, 68260, 178707, 110447 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,1,0,1).

FORMULA

a(n)= a(n-2) +a(n-4). G.f.: x*(-2-3*x-3*x^2+x^3)/(-1+x^2+x^4). a(2n+1) = A001060(n). a(2n) = A013655(n-1). [From R. J. Mathar, Apr 14 2010]

a(n)=x(n) = -1/4 * (1/2 + 1/2 * sqrt(5))^(1/2 * n) * (1/2 + 1/2 * sqrt(5))^(1/4 * (-1)^n) * (-1)^n * (1/2 + 1/2 * sqrt(5))^(-1/4) + 9/20 * (1/2 + 1/2 * sqrt(5))^(1/2 * n) * (1/2 + 1/2 * sqrt(5))^(1/4 * (-1)^n) * (1/2 + 1/2 * sqrt(5))^(-1/4) * sqrt(5) + 5/4 * (1/2-1/2 * sqrt(5))^(-1/4) * (1/2-1/2 * sqrt(5))^(1/2 * n) * (1/2-1/2 * sqrt(5))^(1/4 * (-1)^n)-9/20 * (1/2-1/2 * sqrt(5))^(-1/4) * (1/2-1/2 * sqrt(5))^(1/2 * n) * (1/2-1/2 * sqrt(5))^(1/4 * (-1)^n) * sqrt(5)-1/4 * (-1)^n * (1 /2-1/2 * sqrt(5))^(-1/4) * (1/2-1/2 * sqrt(5))^(1/2 * n) * (1/2-1/2 * sqrt(5))^(1/4 * (-1)^n) + 5/4 * (1/2 + 1/2 * sqrt(5))^(1/2 * n) * (1/2 + 1/2 * sqrt(5))^(1/4 * (-1)^n) * (1/2 + 1/2 * sqrt(5))^(-1/4)-7/20 * (-1)^n * (1/2-1/2 * sqrt(5))^(-1/4) * (1/2-1/2 * sqrt(5))^(1/2 * n) * (1/2-1/2 * sqrt(5))^(1/4 * (-1)^n) * sqrt(5) + 7/20 * (1/2 + 1/2 * sqrt(5))^(1/2 * n) * (1/2 + 1/2 * sqrt(5))^(1/4 * (-1)^n) * (-1)^n * (1/2 + 1/2 * sqrt(5))^(-1/4) * sqrt(5), with n>=0 [From Paolo P. Lava, Apr 23 2010]

MATHEMATICA

nxt[{n_, a_, b_}]:={n+1, b, If[EvenQ[n], b-a, b+a]}; Transpose[ NestList[ nxt, {1, 2, 3}, 50]][[2]] (* or *) LinearRecurrence[{0, 1, 0, 1}, {2, 3, 5, 2}, 51] (* Harvey P. Dale, Jan 06 2012 *)

CROSSREFS

Sequence in context: A096062 A176195 A231233 * A224382 A069227 A117368

Adjacent sequences:  A174559 A174560 A174561 * A174563 A174564 A174565

KEYWORD

easy,nonn

AUTHOR

Giovanni Teofilatto, Mar 22 2010

EXTENSIONS

a(44) corrected by R. J. Mathar, Apr 14 2010

Precise definition from R. J. Mathar, Aug 23 2010

STATUS

approved

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Last modified September 20 09:44 EDT 2021. Contains 347583 sequences. (Running on oeis4.)