OFFSET
1,2
COMMENTS
p(x,n) is a strong divisibility sequence of polynomials. That is, gcd(p(x,h),p(x,k)) = p(x,gcd(h,k)). If x is an integer, then p(x,n) is a strong divisibility sequence of integers.
EXAMPLE
First six rows:
1;
3, 4;
7, 18, 12;
15, 56, 72, 32;
31, 150, 280, 240, 80;
63, 372, 900, 1120, 720, 192;
The first six polynomials, not factored:
1, 3 + 4 x, 7 + 18 x + 12 x^2, 15 + 56 x + 72 x^2 + 32 x^3, 31 + 150 x + 280 x^2 + 240 x^3 + 80 x^4, 63 + 372 x + 900 x^2 + 1120 x^3 + 720 x^4 + 192 x^5.
The first six polynomials, factored:
1, 3 + 4 x, 7 + 18 x + 12 x^2, (3 + 4 x) (5 + 12 x + 8 x^2), 31 + 150 x + 280 x^2 + 240 x^3 + 80 x^4, (3 + 4 x) (3 + 6 x + 4 x^2) (7 + 18 x + 12 x^2).
MATHEMATICA
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Nov 08 2019
STATUS
approved