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A141679
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Triangle of coefficients of the inverse of A058071.
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0
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1, -1, 1, -1, -1, 1, 0, -1, -1, 1, 0, 0, -1, -1, 1, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1
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OFFSET
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1,1
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COMMENTS
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The row sums are {1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, ...}.
The inverse is a tridiagonal lower triangular matrix.
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LINKS
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Table of n, a(n) for n=1..66.
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FORMULA
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A058071(n,m)=If[m <= n, Fibonacci[n - m + 1]*Fibonacci[m + 1], 0]; t(n,m)=Fibonacci(n)*Inverse[A058071(n,m)].
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EXAMPLE
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{1},
{-1, 1},
{-1, -1, 1},
{0, -1, -1, 1},
{0, 0, -1, -1, 1},
{0, 0,0, -1, -1, 1},
{0, 0, 0, 0, -1, -1, 1},
{0, 0, 0, 0, 0, -1, -1, 1},
{0, 0, 0, 0, 0, 0, -1, -1, 1},
{0, 0, 0, 0, 0, 0, 0, -1, -1, 1},
{0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1}
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MATHEMATICA
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Clear[t, n, m, M] (*A058071*) t[n_, m_] = If[m <= n, Fibonacci[n - m + 1]*Fibonacci[m + 1], 0]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]; M = Inverse[Table[Table[t[n, m], {m, 0, 10}], {n, 0, 10}]]; Table[Table[Fibonacci[n]*M[[n, m]], {m, 1, n}], {n, 1, 11}]; Flatten[%]
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CROSSREFS
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Cf. A058071.
Sequence in context: A129572 A070950 A071031 * A152904 A071033 A118102
Adjacent sequences: A141676 A141677 A141678 * A141680 A141681 A141682
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KEYWORD
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tabl,sign
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AUTHOR
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Roger L. Bagula and Gary W. Adamson, Sep 07 2008
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EXTENSIONS
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Edited by N. J. A. Sloane, Jan 05 2009
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STATUS
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approved
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