A104723 Moebius transform of Jacobsthal numbers.

0, 1, 0, 2, 4, 10, 18, 42, 80, 168, 330, 682, 1340, 2730, 5418, 10910, 21760, 43690, 87192, 174762, 349180, 699006, 1397418, 2796202, 5590960, 11184800, 22366890, 44739072, 89473020, 178956970, 357902670, 715827882, 1431633920, 2863310846

Offset: 0

Author

Paul Barry, Mar 20 2005

Keywords

• nonn

Crossrefs

Cf. A001045, A309729.

Formula

a(n) = Sum_{d|n} mu(n/d)*A001045(d).

a(n+3) = 3*A027375(n+3) (since the Moebius transform of (-1)^n is (-1, -1, 2, 0, 0, 0, ...)).

G.f.: Sum_{k>=1} mu(k) * x^k / (1 - x^k - 2*x^(2*k)). - Ilya Gutkovskiy, Feb 06 2020