A290750 Inverse Euler transform of [3, 13, 55, 233, 987, 4181, 17711, 75025, 317811, ...], Fibonacci(3*k+1).

3, 7, 24, 76, 272, 948, 3496, 12920, 48792, 185912, 716472, 2781600, 10878640, 42789292, 169181280, 671865840, 2678679360, 10716650484, 43007271768, 173072547360, 698235684336, 2823329204964, 11439823954664, 46440709197120, 188856966713360, 769241291697640, 3137871076653336, 12817512478814400

Offset: 1

Author

N. J. A. Sloane, Aug 12 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• Latham Boyle, Paul J. Steinhardt, Self-Similar One-Dimensional Quasilattices, arXiv preprint arXiv:1608.08220 [math-ph], 2016. See Table 2, column 8.
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A033887.

Programs

Maple

read(transforms): with(combinat); F:=fibonacci;
s1:=[seq(F(3*n+1),n=1..40)];
EULERi(s1);

Mathematica

mob[m_, n_] := If[Mod[m, n] == 0, MoebiusMu[m/n], 0];
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]];
EULERi[Table[Fibonacci[3k + 1], {k, 1, 30}]] (* Jean-François Alcover, Aug 06 2018 *)

Formula

a(n) ~ (2 + sqrt(5))^n / n. - Vaclav Kotesovec, Oct 09 2019