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 A080116 Characteristic function of A014486. a(n) = 1 if n's binary expansion is totally balanced, otherwise zero. 6
 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS a(n) = 1 if the binary representation of n forms a valid Dyck path, or equally, a well-formed parenthesization when 1's are converted to left and 0's to right parentheses (that is, when A007088(n) is in A063171), and 0 otherwise. - Antti Karttunen, Aug 23 2019 LINKS Antti Karttunen, Table of n, a(n) for n = 0..65537 EXAMPLE 0 stands for an empty parenthesization, thus a(0) = 1. 2 has binary expansion "10", which corresponds with "()", thus a(2) = 1. 3 has binary expansion "11", but "((" is not a well-formed parenthesization, thus a(3) = 0. 10 has binary expansion "1010", corresponding with a well-formed parenthesization "()()", thus a(10) = 1. 38 has binary expansion "100110", but "())(()" is not a well-formed parenthesization, thus a(38) = 0. MAPLE A080116 := proc(n) local c, lev; lev := 0; c := n; while(c > 0) do lev := lev + (-1)^c; c := floor(c/2); if(lev < 0) then RETURN(0); fi; od; if(lev > 0) then RETURN(0); else RETURN(1); fi; end; MATHEMATICA A080116[n_] := (lev = 0; c = n; While[c > 0, lev = lev + (-1)^c; c = Floor[c/2]; If[lev < 0, Return]]; If[lev > 0, Return, Return]); Table[A080116[n], {n, 0, 104}] (* Jean-François Alcover, Jul 24 2013, translated from Maple *) PROG (Sage) def A080116(n) :     lev = 0     while n > 0 :         lev += (-1)^n         if lev < 0: return 0         n = n//2     return 0 if lev > 0 else 1 [A080116(n) for n in (0..104)] # Peter Luschny, Aug 09 2012 (PARI) A080116(n) = { my(k=0); while(n, k += (-1)^n; n >>= 1; if(k<0, return(0))); (0==k); }; \\ Antti Karttunen, Aug 23 2019 CROSSREFS Cf. A014486, A063171, A080110, A080111, A080300, A080301. Sequence in context: A016378 A323513 A089805 * A016359 A014029 A016396 Adjacent sequences:  A080113 A080114 A080115 * A080117 A080118 A080119 KEYWORD nonn,base AUTHOR Antti Karttunen Feb 11 2003 EXTENSIONS Examples added by Antti Karttunen, Aug 23 2019 STATUS approved

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Last modified November 20 14:54 EST 2019. Contains 329337 sequences. (Running on oeis4.)