OFFSET
0,1
COMMENTS
6n + 5 = (12n + 10) / 2 is never a square, as 5 is not a quadratic residue modulo 6. Using this, we can show that each term has an even square part and an even squarefree part, neither part being a power of 2. (Less than 2% of integers have this property - see A339245.) - Peter Munn, Dec 14 2020
LINKS
Eric Weisstein's World of Mathematics, Quadratic Residue.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) with a(0)=1000, a(1)=10648, a(2)=39304, a(3)=97336. [Harvey P. Dale, Sep 30 2011]
MAPLE
MATHEMATICA
(12Range[0, 30]+10)^3 (* or *) LinearRecurrence[{4, -6, 4, -1}, {1000, 10648, 39304, 97336}, 30] (* Harvey P. Dale, Sep 30 2011 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved