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%I #8 Aug 10 2015 07:30:59
%S 1,2,3,4,6,8,11,16,24,35,52,77,114,170,255,385,584,889,1358,2081,3199,
%T 4932,7625,11818,18357,28568,44530,69504,108607,169869,265899,416507,
%U 652845,1023946,1607064,2524042,3967246,6240680,9825202,15481988,24416684,38539840,60880090
%N a(n) = number of steps required to reach 0 from F(n+2) 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 a(n) = A219642(A000045(n+2)).
%F a(0) = 1; for n >= 1, a(n) = A261091(n) + a(n-1).
%F Other identities. For all n >= 0:
%F a(n) = A261081(n)+1.
%o (Scheme, two alternatives, the other one using memoizing definec-macro)
%o (define (A261082 n) (A219642 (A000045 (+ 2 n))))
%o (definec (A261082 n) (if (zero? n) 1 (+ (A261091 n) (A261082 (- n 1)))))
%Y One more than A261081.
%Y First differences give A261091.
%Y Cf. A000045, A219642, A261102.
%K nonn
%O 0,2
%A _Antti Karttunen_, Aug 08 2015
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