login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Triangle of coefficients of the inverse of A058071.
2

%I #9 Jun 05 2018 22:33:11

%S 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,

%T 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,

%U 0,0,0,-1,-1,1

%N Triangle of coefficients of the inverse of A058071.

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

%C The inverse is a tridiagonal lower triangular matrix.

%H G. C. Greubel, <a href="/A141679/b141679.txt">Rows n=1..100 of triangle, flattened</a>

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

%e {1},

%e {-1, 1},

%e {-1, -1, 1},

%e {0, -1, -1, 1},

%e {0, 0, -1, -1, 1},

%e {0, 0,0, -1, -1, 1},

%e {0, 0, 0, 0, -1, -1, 1},

%e {0, 0, 0, 0, 0, -1, -1, 1},

%e {0, 0, 0, 0, 0, 0, -1, -1, 1},

%e {0, 0, 0, 0, 0, 0, 0, -1, -1, 1},

%e {0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1}

%t 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[%]

%Y Cf. A058071.

%Y As a sequence, quite similar to A136705. - _N. J. A. Sloane_, Dec 14 2014

%K tabl,sign

%O 1,1

%A _Roger L. Bagula_ and _Gary W. Adamson_, Sep 07 2008

%E Edited by _N. J. A. Sloane_, Jan 05 2009