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Run lengths in A219652.
7

%I #7 Nov 25 2012 23:56:30

%S 1,1,2,2,2,4,4,4,4,2,4,4,4,4,6,4,4,4,6,6,6,6,6,6,6,6,8,4,2,4,4,4,4,6,

%T 4,4,4,6,6,6,6,6,6,6,6,8,6,8,8,6,4,4,4,6,6,6,6,6,6,6,6,8,6,8,8,6,8,10,

%U 6,6,6,6,6,6,6,8,6,8,8,6,8,10,8,10,12,6

%N Run lengths in A219652.

%C a(n) tells from how many starting values one can end to 0 in n steps, with the iterative process described in A219652 (if going around in 0->0 loop is disallowed).

%H A. Karttunen, <a href="/A219654/b219654.txt">Table of n, a(n) for n = 0..10080</a>

%F a(n) = A219653(n+1)-A219653(n). (The first differences of A219653).

%o (Scheme with two different variants):

%o (define (A219654 n) (- (A219653 (1+ n)) (A219653 n)))

%o (define (A219654v2 n) (1+ (- (A219655 n) (A219653 n))))

%Y a(n) = 1+(A219655(n)-A219653(n)). This sequence is based on Factorial number system: A007623. Analogous sequence for binary system: A086876, for Zeckendorf expansion: A219644. Cf. A219652, A219659, A219666.

%K nonn

%O 0,3

%A _Antti Karttunen_, Nov 25 2012