This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A127284 #5 Jul 24 2025 18:38:33 %S A127284 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 A127284 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 A127284 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 A127284 a(n) = number of valleys (DU-steps) in the Dyck path encoded by A014486(n). %F A127284 a(0)=0, a(n) = A057514(n)-1. %e A127284 A014486(2) = 10 (1010 in binary) which encodes Dyck path /\/\ with two peaks and one valley, thus a(2)=1. %e A127284 A014486(12) = 180 (10110100 in binary) which encodes Dyck path: %e A127284 ..../\/\... %e A127284 ./\/....\.. %e A127284 which has two valleys, thus a(12) = 2. %o A127284 (Scheme) (define (A127284 n) (if (zero? n) 0 (- (A057514 n) 1))) %Y A127284 a(A057163(n)) = A126306(n), a(n) = A126306(A057163(n)) for all n. Cf. A057516. %K A127284 nonn %O A127284 0,5 %A A127284 _Antti Karttunen_, Jan 16 2007