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%I #18 Oct 09 2019 03:12:42
%S 3,7,24,76,272,948,3496,12920,48792,185912,716472,2781600,10878640,
%T 42789292,169181280,671865840,2678679360,10716650484,43007271768,
%U 173072547360,698235684336,2823329204964,11439823954664,46440709197120,188856966713360,769241291697640,3137871076653336,12817512478814400
%N Inverse Euler transform of [3, 13, 55, 233, 987, 4181, 17711, 75025, 317811, ...], Fibonacci(3*k+1).
%H Alois P. Heinz, <a href="/A290750/b290750.txt">Table of n, a(n) for n = 1..1000</a>
%H Latham Boyle, Paul J. Steinhardt, <a href="https://arxiv.org/abs/1608.08220">Self-Similar One-Dimensional Quasilattices</a>, arXiv preprint arXiv:1608.08220 [math-ph], 2016. See Table 2, column 8.
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F a(n) ~ (2 + sqrt(5))^n / n. - _Vaclav Kotesovec_, Oct 09 2019
%p read(transforms): with(combinat); F:=fibonacci;
%p s1:=[seq(F(3*n+1),n=1..40)];
%p EULERi(s1);
%t mob[m_, n_] := If[Mod[m, n] == 0, MoebiusMu[m/n], 0];
%t EULERi[b_] := Module[{a, c, i, d}, c = {}; For[i = 1, i <= Length[b], i++, c = Append[c, i b[[i]] - Sum[c[[d]] b[[i - d]], {d, 1, i - 1}]]]; a = {}; For[i = 1, i <= Length[b], i++, a = Append[a, (1/i)*Sum[mob[i, d] c[[d]], {d, 1, i}]]]; Return[a]];
%t EULERi[Table[Fibonacci[3k + 1], {k, 1, 30}]] (* _Jean-François Alcover_, Aug 06 2018 *)
%Y Cf. A033887.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Aug 12 2017
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