

A181347


Numerators of lower triangular matrix T:=log(F), with the matrix F:=A037027 (Fibonacci convolution matrix).


2



0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 1, 3, 4, 0, 2, 2, 3, 4, 5, 0, 2, 4, 1, 2, 5, 6, 0, 31, 4, 2, 4, 5, 6, 7, 0, 3, 31, 2, 8, 5, 3, 7, 8, 0, 202, 3, 31, 8, 10, 2, 7, 8, 9, 0, 4, 404, 9, 62, 2, 4, 7, 4, 9, 10, 0, 464, 8, 202, 6, 31, 4, 14, 8, 9, 10, 11, 0, 2048, 928, 12, 808, 3, 31, 14, 16, 3, 5, 11, 12, 0
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OFFSET

0,5


COMMENTS

The denominator triangle is given by A181348.
Because exp(T) = F, T may be considered as generator of F.
This should be read as N x N matrix for N>=2: log(F_N) := sum(((1)^k)/k)*(F_N  Id_N)^k,N1) with the lower triangular N x N matrix F_N := Matrix([seq([seq(A037027(n,m),n=0..N1)],m=0..N1)]) and the N x N identity matrix Id_N.
The log series terminates because of the lower triangular property, and the fact that all main diagonal elements are 1, which follows from
F = Riordan matrix (Fib(x),x*Fib(x)) with the o.g.f. Fib(x)=1/(1xx^2). For this notation of Riordan arrays see, e.g., the W.Lang link given in A006232, and there the paragraph "Summary on A and Zsequences for Riordan matrices", as well as the 1991 Shapiro et al. reference on the Riordan group given in A053121.


LINKS

Table of n, a(n) for n=0..90.
Wolfdieter Lang, A181347/A181348, Logarithm of the Fibonacci matrix A037027


FORMULA

a(n,m) = numerator((log F)(n,m)), with the Fibonacci lower triangular matrix F=A037027.


EXAMPLE

[0]; [1,0]; [1,2,0]; [1,2,3,0]; [1,1,3,4,0];...
The rational triangle (with main diagonal elements 0) starts with the rows [0]; [1, 0]; [1, 2, 0]; [1/2, 2, 3, 0]; [1/3, 1, 3, 4, 0];...


CROSSREFS

Sequence in context: A336937 A069584 A199238 * A014587 A025658 A025673
Adjacent sequences: A181344 A181345 A181346 * A181348 A181349 A181350


KEYWORD

sign,easy,tabl


AUTHOR

Wolfdieter Lang, Oct 15 2010


STATUS

approved



