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Search: id:A141679
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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
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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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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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: A111940 A129572 A070950 this_sequence A071027 A152904 A118102
Adjacent sequences: A141676 A141677 A141678 this_sequence 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 (rlbagulatftn(AT)yahoo.com), Sep 07 2008
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Jan 05 2009
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