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A081420 Let f(1)=f(2)=1, f(k)=f(k-1)+f(k-2)+ (k (mod n)). Then f(k)=floor(r(n)*F(k))+g(k) where F(k) denotes the k-th Fibonacci number and g(k) a function becoming periodic. Sequence depends on r(n) which is the largest positive root of : a(3n-2)*X^2-a(3n-1)*X+a(3n)=0. 0

%I

%S 0,1,1,1,1,1,4,18,19,5,25,31,11,64,89,4,24,31,29,184,236,45,285,319,

%T 76,486,499,121,759,639,199,1230,855,20,120,59,521,3038,916,841,4727,

%U 341,1364,7386,1189,2205,11445,4889

%N Let f(1)=f(2)=1, f(k)=f(k-1)+f(k-2)+ (k (mod n)). Then f(k)=floor(r(n)*F(k))+g(k) where F(k) denotes the k-th Fibonacci number and g(k) a function becoming periodic. Sequence depends on r(n) which is the largest positive root of : a(3n-2)*X^2-a(3n-1)*X+a(3n)=0.

%C Usually a(3n-2)=A001350(n)

%F It seems that limit n-->infinity r(n)=(9+sqrt(5))/2

%e If n=3 f(k)=floor(r(3)*F(k))+g(k) where r(3)=(9-sqrt(5))/4 is the root of 4*X^2-18*X+19=0 and g(k) is the 6-periodic sequence (0,0,-1,-1,0,-1)

%K nonn

%O 1,7

%A _Benoit Cloitre_, Apr 20 2003

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Last modified July 25 01:31 EDT 2021. Contains 346273 sequences. (Running on oeis4.)