OFFSET
0,2
COMMENTS
In the language of the Shapiro et al. reference (given in A053121) such a lower triangular (ordinary) convolution array, considered as a matrix, belongs to the Riordan-group. The G.f. for the row polynomials p(n,x) (increasing powers of x) is ((Pell(z))^2)/(Fib(z)*(1-x*z*Fib(z))) with Pell(x)=1/(1-2*x-x^2) = g.f. for A000129(n+1) (Pell numbers without 0) and Fib(x)=1/(1-x-x^2) = g.f. for A000045(n+1) (Fibonacci numbers without 0).
This is the second member of the family of Riordan-type matrices obtained from the Fibonacci convolution matrix A037027 by repeated application of the partial row sums procedure.
FORMULA
EXAMPLE
{1}; {3,1}; {9,4,1}; {26,14,5,1};...
Fourth row polynomial (n=3): p(3,x)= 26+14*x+5*x^2+x^3
CROSSREFS
KEYWORD
AUTHOR
Wolfdieter Lang, Apr 27 2000 and May 08 2000.
STATUS
approved