cp's OEIS Frontend

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.

%I A081420 #6 Mar 30 2012 18:39:16
%S A081420 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 A081420 76,486,499,121,759,639,199,1230,855,20,120,59,521,3038,916,841,4727,
%U A081420 341,1364,7386,1189,2205,11445,4889
%N 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.
%C A081420 Usually a(3n-2)=A001350(n)
%F A081420 It seems that limit n-->infinity r(n)=(9+sqrt(5))/2
%e A081420 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 A081420 nonn
%O A081420 1,7
%A A081420 _Benoit Cloitre_, Apr 20 2003