A357239 Inverse Moebius transform of tetranacci number (A000078).

0, 0, 1, 1, 2, 5, 8, 16, 30, 58, 108, 214, 401, 781, 1493, 2888, 5536, 10705, 20569, 39707, 76433, 147420, 283953, 547566, 1055028, 2034029, 3919974, 7556717, 14564533, 28075593, 54114452, 104311848, 201062094, 387564973, 747044844, 1439986130, 2775641472, 5350241528, 10312882883

Offset: 1

Author

Ilya Gutkovskiy, Sep 19 2022

Keywords

• nonn

Crossrefs

Cf. A000078, A007435, A357238.

Programs

Mathematica

nmax = 39; CoefficientList[Series[Sum[x^(3 k)/(1 - x^k - x^(2 k) - x^(3 k) - x^(4 k)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Formula

G.f.: Sum_{k>=1} x^(3*k) / (1 - x^k - x^(2*k) - x^(3*k) - x^(4*k)).

G.f.: Sum_{k>=1} A000078(k) * x^k / (1 - x^k).

a(n) = Sum_{d|n} A000078(d).