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1, -2, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, 0, 1, 1, -1, 0, 0, 1, 0, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, 1, 1, 0, -1, -1, -1, 0, 0, 1, -1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 1, 1, -1, 0, -1, 1, 0, 0, 1, -1, -1, 0, 1, -1, -1, 0, -1, 1, 0, 0, 1, -1, -1, 0, 0, 1, -1, 0, 1, 1, 1, 0, -1, 0, 1, 0
(list;
graph;
refs;
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internal format)
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OFFSET
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1,2
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COMMENTS
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Except for the second term, a(n) seems to be equal to the Mobius function mu(n) = A008683(n) (verified for the first 53 terms).
a(n) = A008683(n) has now been verified for 3 <= n <= 800. - R. J. Mathar, Sep 14 2017
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..800 (prepared from the b-file of A008683 based on R. J. Mathar's Sep 14 2017 comment)
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FORMULA
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a(n) = A178535(n,1).
a(n) = Sum_{k|n} A008683(n/k)*([k = 1] - [2|k]) (conjecture). - Mats Granvik, Jan 24 2021
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MAPLE
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A178536 := proc(n) A178535(n, 1) ; end proc;
seq(A178536(n), n=1..80) ; # R. J. Mathar, Oct 28 2010
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MATHEMATICA
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Clear[t, n, k, nn, a, A]; nn=92; a = Fibonacci[Range[nn] + 1]; t[n_, 1] = If[n >= 1, a[[n]], 0]; t[n_, k_] := t[n, k] = If[n >= k, Sum[t[n - i, k - 1], {i, 1, k - 1}] - Sum[t[n - i, k], {i, 1, k - 1}], 0]; MatrixForm[A = Table[Table[t[n, k], {k, 1, nn}], {n, 1, nn}]]; Inverse[A][[All, 1]] (* Mats Granvik, Sep 15 2017 *)
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CROSSREFS
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Cf. A178535, A008683.
Cf. also A181434, A181435.
Sequence in context: A296139 A321763 A280126 * A286656 A048484 A298601
Adjacent sequences: A178533 A178534 A178535 * A178537 A178538 A178539
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KEYWORD
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sign
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AUTHOR
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Mats Granvik, May 29 2010
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EXTENSIONS
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More terms from R. J. Mathar, Oct 28 2010
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STATUS
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approved
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