A072800 Composition of A030101 and A014486. Binary encodings of parenthesizations, Dyck paths and other Catalan structures reversed.

0, 1, 5, 3, 21, 13, 19, 11, 7, 85, 53, 77, 45, 29, 83, 51, 75, 43, 27, 71, 39, 23, 15, 341, 213, 309, 181, 117, 333, 205, 301, 173, 109, 285, 157, 93, 61, 339, 211, 307, 179, 115, 331, 203, 299, 171, 107, 283, 155, 91, 59, 327, 199, 295, 167, 103, 279, 151, 87, 55

Offset: 0

Author

Antti Karttunen, Jun 12 2002

Keywords

• nonn
• frac
• base
• look

Comments

See A014486.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..23713
• Dana G. Korssjoen, Biyao Li, Stefan Steinerberger, Raghavendra Tripathi, and Ruimin Zhang, Finding structure in sequences of real numbers via graph theory: a problem list, arXiv:2012.04625 [math.CO], 2020-2021. See numerators of fractions in Section 2.8. (For denominators see A339570.)
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to parenthesizing

Crossrefs

Cf. A014486, A030101, A339570 (gives the denominators).

Programs

PARI

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
A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));
k=0; n=0; while(k<23714, if(isA014486(n), write("b072800.txt", k, " ", A030101(n)); k++); n++); \\ Antti Karttunen, Mar 28 2022

Formula

a(n) = A030101(A014486(n)).