|
|
A158587
|
|
a(n) = 289*n^2 - 17.
|
|
2
|
|
|
272, 1139, 2584, 4607, 7208, 10387, 14144, 18479, 23392, 28883, 34952, 41599, 48824, 56627, 65008, 73967, 83504, 93619, 104312, 115583, 127432, 139859, 152864, 166447, 180608, 195347, 210664, 226559, 243032, 260083, 277712, 295919, 314704, 334067, 354008, 374527
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The identity (34*n^2 - 1)^2 - (289*n^2 - 17) * (2*n)^2 = 1 can be written as A158588(n)^2 - a(n) * A005843(n)^2 = 1.
|
|
LINKS
|
Vincenzo Librandi, X^2-AY^2=1, Math Forum, 2007. [Wayback Machine link]
|
|
FORMULA
|
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: 17*x*(-16 - 19*x + x^2)/(x-1)^3.
Sum_{n>=1} 1/a(n) = (1 - cot(Pi/sqrt(17))*Pi/sqrt(17))/34.
Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(17))*Pi/sqrt(17) - 1)/34. (End)
|
|
MATHEMATICA
|
LinearRecurrence[{3, -3, 1}, {272, 1139, 2584}, 50] (* Vincenzo Librandi, Feb 15 2012 *)
|
|
PROG
|
(Magma) I:=[272, 1139, 2584]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 15 2012
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|