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Run lengths in A219642.
5

%I #7 Nov 25 2012 23:49:09

%S 1,1,1,2,2,1,2,3,2,3,3,2,3,3,3,2,2,3,3,3,2,3,4,1,2,3,3,3,2,3,4,3,3,3,

%T 5,2,3,3,3,2,3,4,3,3,3,5,3,4,4,4,5,1,2,3,3,3,2,3,4,3,3,3,5,3,4,4,4,5,

%U 3,3,3,5,5,3,5,5,3,2,3,3,3,2,3,4,3,3,3

%N Run lengths in A219642.

%C a(n) tells from how many starting values one can end to 0 in n steps, with the iterative process described in A219642 (if going around in 0->0 loop is disallowed).

%H A. Karttunen, <a href="/A219644/b219644.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = A219643(n+1)-A219643(n). (The first differences of A219643).

%o (Scheme, with two different variants):

%o (define (A219644 n) (- (A219643 (1+ n)) (A219643 n)))

%o (define (A219644v2 n) (1+ (- (A219645 n) (A219643 n))))

%Y a(n) = 1+(A219645(n)-A219643(n)).

%Y This sequence is based on Fibonacci number system (Zeckendorf expansion): A014417. Analogous sequence for binary system: A086876, for factorial number system: A219654.

%K nonn

%O 0,4

%A _Antti Karttunen_, Nov 24 2012