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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, Table of n, a(n) for n = 0..1000 Vincenzo Librandi, X^2-AY^2=1, Math Forum, 2007. [Wayback Machine link] Index entries for linear recurrences with constant coefficients, signature (3,-3,1). 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 Cf. A005843, A158686. Sequence in context: A009976 A144319 A041481 * A265021 A159360 A249392 Adjacent sequences: A158682 A158683 A158684 * A158686 A158687 A158688 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.)