OFFSET
0,1
COMMENTS
The product of eight consecutive positive integers can always be expressed as the difference of two squares: x^2 - y^2.
This sequence gives the x-values for each product. The y-values are A017113(n+4).
a(n) is always divisible by 4. In addition, we have (a(n)+16)/4 belongs to A028387.
Are 4 and 8 the unique values of k such that the product of k consecutive integers is always distant to upper square by a square?
LINKS
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
G.f.: 4*(7 + 16*x - 34*x^2 + 22*x^3 - 5*x^4)/(1 - x)^5. - Stefano Spezia, Jul 14 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Lamine Ngom, Jul 14 2021
STATUS
approved