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A080300 Global ranking function for totally balanced binary sequences. 53
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 3, 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, 4, 0, 5, 0, 0, 0, 0, 0, 6, 0, 7, 0, 0, 0, 8, 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
0,11
COMMENTS
Note: the next nonzero value occurs at a(170)=9, as 170 = 10101010 is the lexicographically earliest totally balanced binary sequence of length 2*4.
LINKS
A. Karttunen, Catalan ranking and unranking functions, OEIS Wiki.
Various authors, Source code for Catalan ranking and unranking functions (in various programming languages), OEIS Wiki.
FORMULA
a(n) = A080116(n)*A215406(n).
a(n) = 0 if n=0 or (A080116(n)=0), otherwise a(n) = A014137(((A000523(n)+1)/2)-1)+A080301(n)
MAPLE
A080300 := n -> A080116(n)*A215406(n); # Untested (as of Aug 19 2012)
A080300 := n -> `if`((0 = n) or (0 = A080116(n)), 0, A014137(((A000523(n)+1)/2)-1)+A080301(n));
MATHEMATICA
A080116[n_] := Module[{lev = 0, c = n}, While[c > 0, lev = lev + (-1)^c; c = Floor[c/2]; If[lev<0, Return[0]]]; If[lev>0, Return[0], Return[1]]];
A215406[n_] := Module[{m, d, a, y, t, x, u, v}, m = Quotient[Length[d = IntegerDigits[n, 2]], 2]; a = FromDigits[Reverse[d], 2]; y = 0; t = 1; For[x = 0, x <= 2*m - 2, x++, If[Mod[a, 2] == 1, y++, u = 2*m - x; v = m - Quotient[x + y, 2] - 1; t = t - Binomial[u - 1, v - 1] + Binomial[u - 1, v]; y--]; a = Quotient[a, 2]]; (1 - I*Sqrt[3])/2 - 4^(m + 1)*Gamma[m + 3/2]*Hypergeometric2F1[1, m + 3/2, m + 3, 4]/(Sqrt[Pi]*Gamma[m + 3]) -t];
a[n_] := A080116[n]*A215406[n] // Simplify;
Table[a[n], {n, 0, 170}] (* Jean-François Alcover, Mar 05 2016 *)
PROG
(See the Source code... page at OEIS Wiki! Please add your code there, if possible.)
CROSSREFS
Inverse function of A014486, i.e. a(A014486(n)) = n for all n. Cf. A080116, A215406, A213704, A209640.
Sequence in context: A013371 A013372 A209640 * A116864 A255308 A079302
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 21 2003
STATUS
approved

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Last modified February 21 02:30 EST 2024. Contains 370219 sequences. (Running on oeis4.)