A045653 Number of 2n-bead balanced binary strings, rotationally equivalent to reverse.

1, 2, 6, 8, 38, 52, 216, 268, 1062, 1232, 4956, 5524, 21848, 24000, 95780, 102808, 410662, 437548, 1748592, 1847524, 7384988, 7759144, 31033404, 32449828, 129774936, 135207552, 540807104, 561629852, 2246432996, 2326762744, 9306937416, 9617286180, 38468731942

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Links

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

Crossrefs

Cf. A000984, A023900, A045662, A045654, A045655, A045656.

Programs

PARI

c(n)={sumdiv(n,d, moebius(d)*d)} \\ A023900
a(n)={if(n<1, n==0, 2*sumdiv(n, d, c(n/d) * d * binomial(d-d%2, d\2)))} \\ Andrew Howroyd, Sep 15 2019

Formula

Inverse Moebius transform of A045662. - Andrew Howroyd, Sep 15 2019

Extensions

Terms a(30) and beyond from Andrew Howroyd, Sep 15 2019