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%I #2 Mar 31 2012 13:21:13
%S 0,0,1,0,2,1,1,1,0,3,2,2,2,1,2,1,2,2,1,1,1,1,0,4,3,3,3,2,3,2,3,3,2,2,
%T 2,2,1,3,2,2,2,1,3,2,3,3,2,2,2,2,1,2,1,2,2,1,2,2,2,1,1,1,1,1,0,5,4,4,
%U 4,3,4,3,4,4,3,3,3,3,2,4,3,3,3,2,4,3,4,4,3,3,3,3,2,3,2,3,3,2,3,3,3,2
%N a(n) = number of valleys (DU-steps) in the Dyck path encoded by A014486(n).
%F a(0)=0, a(n) = A057514(n)-1.
%e A014486(2) = 10 (1010 in binary) which encodes Dyck path /\/\ with two peaks and one valley, thus a(2)=1.
%e A014486(12) = 180 (10110100 in binary) which encodes Dyck path:
%e ..../\/\...
%e ./\/....\..
%e which has two valleys, thus a(12) = 2.
%o (Scheme:) (define (A127284 n) (if (zero? n) 0 (- (A057514 n) 1)))
%Y a(A057163(n)) = A126306(n), a(n) = A126306(A057163(n)) for all n. Cf. A057516.
%K nonn
%O 0,5
%A _Antti Karttunen_, Jan 16 2007
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