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%I A072800 #16 Mar 28 2022 14:09:01
%S A072800 0,1,5,3,21,13,19,11,7,85,53,77,45,29,83,51,75,43,27,71,39,23,15,341,
%T A072800 213,309,181,117,333,205,301,173,109,285,157,93,61,339,211,307,179,
%U A072800 115,331,203,299,171,107,283,155,91,59,327,199,295,167,103,279,151,87,55
%N A072800 Composition of A030101 and A014486. Binary encodings of parenthesizations, Dyck paths and other Catalan structures reversed.
%C A072800 See A014486.
%H A072800 Antti Karttunen, <a href="/A072800/b072800.txt">Table of n, a(n) for n = 0..23713</a>
%H A072800 Dana G. Korssjoen, Biyao Li, Stefan Steinerberger, Raghavendra Tripathi, and Ruimin Zhang, <a href="https://arxiv.org/abs/2012.04625">Finding structure in sequences of real numbers via graph theory: a problem list</a>, arXiv:2012.04625 [math.CO], 2020-2021. See numerators of fractions in Section 2.8. (For denominators see A339570.)
%H A072800 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A072800 <a href="/index/Par#parens">Index entries for sequences related to parenthesizing</a>
%F A072800 a(n) = A030101(A014486(n)).
%o A072800 (PARI)
%o A072800 isA014486(n) = { my(v=binary(n), t=0); for(i=1, #v, t+=if(v[i], 1, -1); if(t<0, return(0))); t==0; }; \\ From A014486
%o A072800 A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));
%o A072800 k=0; n=0; while(k<23714, if(isA014486(n), write("b072800.txt", k, " ", A030101(n)); k++); n++); \\ _Antti Karttunen_, Mar 28 2022
%Y A072800 Cf. A014486, A030101, A339570 (gives the denominators).
%K A072800 nonn,frac,base,look
%O A072800 0,3
%A A072800 _Antti Karttunen_, Jun 12 2002

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