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A141679 Triangle of coefficients of the inverse of A058071. 2
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; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The row sums are {1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, ...}.

The inverse is a tridiagonal lower triangular matrix.

LINKS

G. C. Greubel, Rows n=1..100 of triangle, flattened

FORMULA

A058071(n,m) = if(m <= n, Fibonacci(n - m + 1)*Fibonacci(m + 1), 0), t(n,m) = Fibonacci(n)*Inverse(A058071(n,m)).

EXAMPLE

{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}

MATHEMATICA

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[%]

CROSSREFS

Cf. A058071.

As a sequence, quite similar to A136705. - N. J. A. Sloane, Dec 14 2014

Sequence in context: A187037 A327866 A190230 * A276254 A303300 A249865

Adjacent sequences:  A141676 A141677 A141678 * A141680 A141681 A141682

KEYWORD

tabl,sign

AUTHOR

Roger L. Bagula and Gary W. Adamson, Sep 07 2008

EXTENSIONS

Edited by N. J. A. Sloane, Jan 05 2009

STATUS

approved

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Last modified October 18 22:14 EDT 2019. Contains 328211 sequences. (Running on oeis4.)