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%I #4 Sep 23 2022 03:20:48
%S 0,0,1,1,2,5,8,16,30,58,108,214,401,781,1493,2888,5536,10705,20569,
%T 39707,76433,147420,283953,547566,1055028,2034029,3919974,7556717,
%U 14564533,28075593,54114452,104311848,201062094,387564973,747044844,1439986130,2775641472,5350241528,10312882883
%N Inverse Moebius transform of tetranacci number (A000078).
%F G.f.: Sum_{k>=1} x^(3*k) / (1 - x^k - x^(2*k) - x^(3*k) - x^(4*k)).
%F G.f.: Sum_{k>=1} A000078(k) * x^k / (1 - x^k).
%F a(n) = Sum_{d|n} A000078(d).
%t 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
%Y Cf. A000078, A007435, A357238.
%K nonn
%O 1,5
%A _Ilya Gutkovskiy_, Sep 19 2022
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