A229995 - OEIS

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A229995

Array of coefficients of numerator polynomials of the rational function p(n, x + 1/x), where p(n,x) is the Fibonacci polynomial defined by p(1,x) = 1, p(2,x) = x, p(n,x) = x*p(n-1,x) + p(n-2,x).

1, 1, 0, 1, 1, 0, 3, 0, 1, 1, 0, 5, 0, 5, 0, 1, 1, 0, 7, 0, 13, 0, 7, 0, 1, 1, 0, 9, 0, 25, 0, 25, 0, 9, 0, 1, 1, 0, 11, 0, 41, 0, 63, 0, 41, 0, 11, 0, 1, 1, 0, 13, 0, 61, 0, 129, 0, 129, 0, 61, 0, 13, 0, 1, 1, 0, 15, 0, 85, 0, 231, 0, 321, 0, 231, 0, 85, 0

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OFFSET

0,7

COMMENTS

Deleting the 0's leaves A008288 (Delannoy numbers as a triangle). If r is a zero of p(n,x) then (1/2)(r +- sqrt(r^2 - 4) are zeros of q(n,x).

LINKS

Table of n, a(n) for n=0..77.

EXAMPLE

First 4 rows:

1 0 1

1 0 3 0 1

1 0 5 0 5 0 1