A050872 a(n) = (1/2)*A050871 (row sums of array T in A050870, periodic binary words).

0, 1, 2, 5, 8, 17, 38, 65, 128, 284, 518, 1025, 2168, 4097, 8198, 16907, 32768, 65537, 133088, 262145, 524408, 1056731, 2097158, 4194305, 8421248, 16777712, 33554438, 67239680, 134217848, 268435457, 537396698, 1073741825, 2147483648

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Crossrefs

Cf. A050870, A050871.

Programs

PARI

T(n, k) = binomial(n, k) - sumdiv(gcd(n+!n, k), d, moebius(d)*binomial(n/d, k/d)); \\ A050870
row(n) = vector(n+1, k, k--; T(n, k));
a(n) = n*=2; vecsum(row(n))/2; \\ Michel Marcus, Aug 20 2021

Python

from sympy import mobius, divisors
def A050872(n): return -sum(mobius((n<<1)//d)<Chai Wah Wu, Sep 21 2024

Extensions

a(29) onward corrected by Sean A. Irvine, Aug 20 2021