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;
5, 4;
21, 30, 12;
85, 168, 120, 32;
341, 850, 840, 400, 80;
1365, 4092, 5100, 3360, 1200, 192;
The first six polynomials, not factored:
1, 5 + 4 x, 21 + 30 x + 12 x^2, 85 + 168 x + 120 x^2 + 32 x^3, 341 + 850 x + 840 x^2 + 400 x^3 + 80 x^4, 1365 + 4092 x + 5100 x^2 + 3360 x^3 + 1200 x^4 + 192 x^5.
The first six polynomials, factored:
1, 5 + 4 x, 3 (7 + 10 x + 4 x^2), (5 + 4 x) (17 + 20 x + 8 x^2), 341 + 850 x + 840 x^2 + 400 x^3 + 80 x^4, 3 (5 + 4 x) (7 + 10 x + 4 x^2) (13 + 10 x + 4 x^2).
MATHEMATICA
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Nov 03 2019
STATUS
approved