login
A195549
Hypotenuses of primitive Pythagorean triples in A195547 and A195548.
4
1, 5, 13, 17, 89, 233, 305, 1597, 4181, 5473, 28657, 75025, 98209, 514229, 1346269, 1762289, 9227465, 24157817, 31622993, 165580141, 433494437, 567451585, 2971215073, 7778742049, 10182505537, 53316291173, 139583862445, 182717648081
OFFSET
1,2
COMMENTS
See A195500 for discussion and list of related sequences; see A195547 for Mathematica program.
FORMULA
a(n) = (F(n)^2 + F(n+1)^2)/(2 - ((n+2)^2 mod 3)), F(n) = Fibonacci(n). - Gary Detlefs, Oct 14 2011
Conjectures from Colin Barker, Apr 08 2012: (Start)
a(n) = 18*a(n-3) - a(n-6).
G.f.: x*(1+5*x+13*x^2-x^3-x^4-x^5)/((1-3*x+x^2)*(1+3*x+8*x^2+3*x^3+x^4)). (End)
Conjecture: a(n) is the denominator of the reduced fraction (F(2*n+1)-2)/F(2*n+1), F(n) = Fibonacci(n). - Sébastien Labbé, May 06 2022
MAPLE
with(combinat):f:= n-> fibonacci(n):seq((f(n)^2+f(n+1)^2)/(2-((n+2)^2 mod 3)), n=1..25);
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Sep 20 2011
STATUS
approved