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 A158735 a(n) = 1225*n^2 - 35. 2
 1190, 4865, 10990, 19565, 30590, 44065, 59990, 78365, 99190, 122465, 148190, 176365, 206990, 240065, 275590, 313565, 353990, 396865, 442190, 489965, 540190, 592865, 647990, 705565, 765590, 828065, 892990, 960365, 1030190, 1102465, 1177190, 1254365, 1333990, 1416065 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The identity (70*n^2 - 1)^2 - (1225*n^2 - 35)*(2*n)^2 = 1 can be written as A158736(n)^2 - a(n)*A005843(n)^2 = 1. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..10000 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.: 35*x*(-34 - 37*x + x^2)/(x-1)^3. a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). From Amiram Eldar, Mar 22 2023: (Start) Sum_{n>=1} 1/a(n) = (1 - cot(Pi/sqrt(35))*Pi/sqrt(35))/70. Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(35))*Pi/sqrt(35) - 1)/70. (End) MATHEMATICA LinearRecurrence[{3, -3, 1}, {1190, 4865, 10990}, 50] (* Vincenzo Librandi, Feb 20 2012 *) 1225Range[30]^2-35 (* Harvey P. Dale, May 08 2021 *) PROG (Magma) I:=[1190, 4865, 10990]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 20 2012 (PARI) for(n=1, 40, print1(1225*n^2 - 35", ")); \\ Vincenzo Librandi, Feb 20 2012 CROSSREFS Cf. A005843, A158736. Sequence in context: A233687 A233640 A252643 * A035860 A290843 A298239 Adjacent sequences: A158732 A158733 A158734 * A158736 A158737 A158738 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Mar 25 2009 EXTENSIONS Comment rewritten and formula replaced by R. J. Mathar, Oct 22 2009 STATUS approved

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Last modified September 27 11:23 EDT 2023. Contains 365688 sequences. (Running on oeis4.)