A195549 - OEIS

A195549

Hypotenuses of primitive Pythagorean triples in A195547 and A195548.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

See A195500 for discussion and list of related sequences; see A195547 for Mathematica program.

LINKS

Table of n, a(n) for n=1..28.

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

Cf. A000045, A195500, A195547, A195548, A131534.

Sequence in context: A145040 A361563 A376396 * A294132 A125146 A051900

Adjacent sequences: A195546 A195547 A195548 * A195550 A195551 A195552

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 20 2011

STATUS

approved