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A290750
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Inverse Euler transform of [3, 13, 55, 233, 987, 4181, 17711, 75025, 317811, ...], Fibonacci(3*k+1).
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1
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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
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OFFSET
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1,1
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LINKS
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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
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FORMULA
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a(n) ~ (2 + sqrt(5))^n / n. - Vaclav Kotesovec, Oct 09 2019
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MAPLE
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read(transforms): with(combinat); F:=fibonacci;
s1:=[seq(F(3*n+1), n=1..40)];
EULERi(s1);
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A033887.
Sequence in context: A258308 A148719 A138541 * A148720 A225826 A228992
Adjacent sequences: A290747 A290748 A290749 * A290751 A290752 A290753
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Aug 12 2017
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STATUS
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approved
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