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A045665
Number of 2n-bead balanced binary strings of fundamental period 2n, rotationally equivalent to reverse, complement and reversed complement.
7
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
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
KEYWORD
nonn
STATUS
approved