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 A154358 a(n) = 1250*n^2 - 1800*n + 649. 5
 649, 99, 2049, 6499, 13449, 22899, 34849, 49299, 66249, 85699, 107649, 132099, 159049, 188499, 220449, 254899, 291849, 331299, 373249, 417699, 464649, 514099, 566049, 620499, 677449, 736899, 798849, 863299, 930249 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The identity (1250*n^2 - 1800*n + 649)^2 - (25*n^2 - 36*n + 13)*(250*n - 180)^2 = 1 can be written as a(n)^2 - A154355(n)*A154360(n)^2 = 1. See also the third comment in A154357. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA G.f.: (649 - 1848*x + 3699*x^2)/(1-x)^3. - R. J. Mathar, Jan 05 2011 a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). E.g.f.: (649 - 550*x + 1250*x^2)*exp(x). - G. C. Greubel, Sep 14 2016 MATHEMATICA LinearRecurrence[{3, -3, 1}, {649, 99, 2049}, 50] (* Vincenzo Librandi, Feb 21 2012 *) PROG (PARI) for(n=0, 40, print1(1250*n^2 - 1800*n + 649", ")); \\ Vincenzo Librandi, Feb 21 2012 (Magma) [1250*n^2-1800*n+649: n in [0..40]]; // Bruno Berselli, Sep 15 2016 CROSSREFS Cf. A154359, A154360, A154361, A154355, A154357. Sequence in context: A107551 A202056 A229155 * A252538 A185666 A114047 Adjacent sequences: A154355 A154356 A154357 * A154359 A154360 A154361 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Jan 08 2009 EXTENSIONS Offset and one entry corrected by R. J. Mathar, Jan 05 2011 Librandi's comment rewritten by Bruno Berselli, Dec 13 2011 STATUS approved

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Last modified July 15 07:59 EDT 2024. Contains 374324 sequences. (Running on oeis4.)