cp's OEIS Frontend

A261081 a(n) = number of steps required to reach 0 from F(n+2)-1 by repeatedly subtracting from a natural number the number of ones in its Zeckendorf representation. Here F(n) = the n-th Fibonacci number, F(0) = 0, F(1) = 1, F(2) = 1, F(3) = 2, ...

%I A261081 #8 Aug 10 2015 07:29:38
%S A261081 0,1,2,3,5,7,10,15,23,34,51,76,113,169,254,384,583,888,1357,2080,3198,
%T A261081 4931,7624,11817,18356,28567,44529,69503,108606,169868,265898,416506,
%U A261081 652844,1023945,1607063,2524041,3967245,6240679,9825201,15481987,24416683,38539839,60880089
%N A261081 a(n) = number of steps required to reach 0 from F(n+2)-1 by repeatedly subtracting from a natural number the number of ones in its Zeckendorf representation. Here F(n) = the n-th Fibonacci number, F(0) = 0, F(1) = 1, F(2) = 1, F(3) = 2, ...
%F A261081 a(n) = A219642(A000045(n+2)-1).
%F A261081 a(0) = 0; for n >= 1, a(n) = A261091(n) + a(n-1).
%F A261081 Other identities. For all n >= 0:
%F A261081 a(n) = A261082(n)-1.
%o A261081 (Scheme, two alternatives, the other one using memoizing definec-macro)
%o A261081 (define (A261081 n) (A219642 (- (A000045 (+ 2 n)) 1)))
%o A261081 (definec (A261081 n) (if (zero? n) n (+ (A261091 n) (A261081 (- n 1)))))
%Y A261081 One less than A261082.
%Y A261081 Partial sums of A261091.
%Y A261081 Cf. A000045, A219642, A261102.
%K A261081 nonn
%O A261081 0,3
%A A261081 _Antti Karttunen_, Aug 08 2015