A045665 Number of 2n-bead balanced binary strings of fundamental period 2n, rotationally equivalent to reverse, complement and reversed complement.

1, 2, 4, 6, 16, 30, 36, 98, 128, 252, 300, 682, 720, 1638, 1764, 3690, 4096, 8670, 9072, 19418, 20400, 42630, 45012, 94162, 97920, 204600, 212940, 441504, 458640, 950214, 981900, 2031554, 2097152, 4323198, 4456380, 9174270, 9434880

Offset

0,2

Links

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

Formula

a(n) = 2*n*A045683(n) for n > 0.

a(n) = n * Sum_{d|n, d odd} mu(d) * 2^ceiling(n/(2*d)) for n > 0.

Prog

(PARI) a(n)={if(n<1, n==0, n*sumdiv(n, d, if(d%2, moebius(d)*2^((n/d+1)\2))))} \\ Andrew Howroyd, Oct 01 2019

Crossrefs

Cf. A007727, A045662, A045663, A045664, A045674, A045683.

Sequence in context: A365639 A279480 A363785 * A133492 A045663 A128092

Adjacent sequences: A045662 A045663 A045664 * A045666 A045667 A045668

Keyword

nonn

Author

David W. Wilson

Status

approved