%I A141679
%S A141679 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,
%T A141679 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
%V A141679 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,
%W A141679 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
%N A141679 Triangle of coefficients of the inverse of A058071.
%C A141679 The row sums are {1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, ...}.
%C A141679 The inverse is a tridiagonal lower triangular matrix.
%F A141679 A058071(n,m)=If[m <= n, Fibonacci[n - m + 1]*Fibonacci[m + 1], 0]; t(n,
               m)=Fibonacci(n)*Inverse[A058071(n,m)].
%e A141679 {1},
%e A141679 {-1, 1},
%e A141679 {-1, -1, 1},
%e A141679 {0, -1, -1, 1},
%e A141679 {0, 0, -1, -1, 1},
%e A141679 {0, 0,0, -1, -1, 1},
%e A141679 {0, 0, 0, 0, -1, -1, 1},
%e A141679 {0, 0, 0, 0, 0, -1, -1, 1},
%e A141679 {0, 0, 0, 0, 0, 0, -1, -1, 1},
%e A141679 {0, 0, 0, 0, 0, 0, 0, -1, -1, 1},
%e A141679 {0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1}
%t A141679 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 A141679 Cf. A058071.
%Y A141679 Sequence in context: A111940 A129572 A070950 this_sequence A071027 A152904 
               A118102
%Y A141679 Adjacent sequences: A141676 A141677 A141678 this_sequence A141680 A141681 
               A141682
%K A141679 tabl,sign
%O A141679 1,1
%A A141679 Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 
               07 2008
%E A141679 Edited by N. J. A. Sloane (njas(AT)research.att.com), Jan 05 2009