OFFSET
0,5
COMMENTS
The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = 1 + (x - 1)/f(n-1,x), where f(0,x) = 1.
Every row sum is 1. The first column is purely periodic with period (1,0,-1,-1,0,1).
Conjecture: for n > 2, p(n,x) is irreducible if and only if n is a (prime - 2). More generally, if c is arbitrary and f(n,x) = 1 + (x + c)/f(n-1,x), where f(x,0) = 1, then p(n,x) is irreducible if and only if n is a (prime - 2).
LINKS
Clark Kimberling, Rows 0..100, flattened
EXAMPLE
f(0,x) = 1/1, so that p(0,x) = 1
f(1,x) = x/1, so that p(1,x) = x;
f(2,x) = (-1 + 2 x)/x, so that p(2,x) = -1 + 2 x.
First 6 rows of the triangle of coefficients:
... 1
... 0 ... 1
.. -1 ... 2
.. -1 ... 1 ... 1
... 0 .. -2 ... 3
... 1 .. -4 ... 3 ... 1
MATHEMATICA
CROSSREFS
KEYWORD
tabf,sign,easy
AUTHOR
Clark Kimberling, Oct 24 2014
STATUS
approved