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A158685 a(n) = 32*(32*n^2+1). 2
32, 1056, 4128, 9248, 16416, 25632, 36896, 50208, 65568, 82976, 102432, 123936, 147488, 173088, 200736, 230432, 262176, 295968, 331808, 369696, 409632, 451616, 495648, 541728, 589856, 640032, 692256, 746528, 802848, 861216, 921632, 984096, 1048608, 1115168, 1183776 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
The identity (64n^2+1)^2 - (1024n^2+32)*(2n)^2 = 1 can be written as (A158686(n))^2 - a(n)*(A005843(n))^2 = 1.
LINKS
Vincenzo Librandi, X^2-AY^2=1, Math Forum, 2007. [Wayback Machine link]
FORMULA
G.f.: -32*(1+30*x+33*x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
From Amiram Eldar, Mar 21 2023: (Start)
Sum_{n>=0} 1/a(n) = (coth(Pi/(4*sqrt(2)))*Pi/(4*sqrt(2)) + 1)/64.
Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/(4*sqrt(2)))*Pi/(4*sqrt(2)) + 1)/64. (End)
MATHEMATICA
CoefficientList[Series[ - 32 (1 + 30 x + 33 x^2) / (x - 1)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Sep 11 2013 *)
PROG
(Magma) [32*(32*n^2+1): n in [0..40]]; // Vincenzo Librandi, Sep 11 2013
(PARI) a(n)=32*(32*n^2+1) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Sequence in context: A009976 A144319 A041481 * A265021 A159360 A249392
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 24 2009
EXTENSIONS
Comment rewritten, a(0) added and formula replaced by R. J. Mathar, Oct 22 2009
STATUS
approved

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Last modified June 20 14:54 EDT 2024. Contains 373526 sequences. (Running on oeis4.)