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A045656 Number of 2n-bead balanced binary strings, rotationally equivalent to reverse, complement and reversed complement. 8
1, 2, 6, 8, 22, 32, 48, 100, 150, 260, 336, 684, 784, 1640, 1868, 3728, 4246, 8672, 9372, 19420, 20752, 42736, 45700, 94164, 98832, 204632, 214584, 441764, 460524, 950216, 985968, 2031556, 2101398, 4323888, 4465056, 9174400, 9444988 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..1000

FORMULA

From Andrew Howroyd, Sep 15 2019: (Start)

Inverse Moebius transform of A045665.

a(n) = 2*Sum_{d|n} A023900(n/d)*d*A045674(d) for n > 0. (End)

MATHEMATICA

b[n_] := Module[{t = 0, r = n}, If[n == 0, 1,  While[Mod[r, 2] == 0, r = r/2; t += 2^(r - 1)]; t + 2^Quotient[r, 2]]];

c[n_] := Sum[MoebiusMu[d]*d, {d, Divisors[n]}];

a[n_] := If[n == 0, 1, 2*Sum[c[n/d]*d*b[d], {d, Divisors[n]}]];

a /@ Range[0, 36] (* Jean-François Alcover, Sep 23 2019, from PARI *)

PROG

(PARI) \\ here b(n) is A045674,  c(n) is A023900.

b(n) = if(n<1, n==0, my(t=0, r=n); while(r%2==0, r=r/2; t+=2^(r-1)); t + 2^(r\2));

c(n) = {sumdiv(n, d, moebius(d)*d)}

a(n) = if(n<1, n==0, 2*sumdiv(n, d, c(n/d)*d*b(d))); \\ Andrew Howroyd, Sep 15 2019

CROSSREFS

Cf. A000984, A023900, A045665, A045653, A045654, A045655, A045674.

Sequence in context: A103023 A341732 A111247 * A343256 A129342 A045654

Adjacent sequences:  A045653 A045654 A045655 * A045657 A045658 A045659

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified December 8 20:37 EST 2021. Contains 349596 sequences. (Running on oeis4.)