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 A157375 a(n) = 2401*n^2 - 980*n + 99. 3
 1520, 7743, 18768, 34595, 55224, 80655, 110888, 145923, 185760, 230399, 279840, 334083, 393128, 456975, 525624, 599075, 677328, 760383, 848240, 940899, 1038360, 1140623, 1247688, 1359555, 1476224, 1597695, 1723968, 1855043, 1990920 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The identity (2401*n^2-980*n+99)^2-(49*n^2-20*n +2)*(343*n-70)^2=1 can be written as a(n)^2-A157373(n)*A157374(n)^2=1. - Vincenzo Librandi, Jan 28 2012 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..10000 Vincenzo Librandi, X^2-AY^2=1 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Jan 28 2012 G.f.: x*(-1520-3183*x-99*x^2)/(x-1)^3. - Vincenzo Librandi, Jan 28 2012 E.g.f.: (49*x*(49*x + 29) + 99)*exp(x) - 99. - G. C. Greubel, Feb 04 2018 MATHEMATICA LinearRecurrence[{3, -3, 1}, {1520, 7743, 18768}, 40] (* Vincenzo Librandi, Jan 28 2012 *) Table[2401*n^2 - 980*n + 99, {n, 1, 30}] (* G. C. Greubel, Feb 04 2018 *) CoefficientList[Series[(-1520-3183x-99x^2)/(-1+x)^3, {x, 0, 40}], x] (* Harvey P. Dale, Jul 27 2021 *) PROG (Magma) I:=[1520, 7743, 18768]; [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, Jan 28 2012 (PARI) for(n=1, 40, print1(2401*n^2 - 980*n + 99", ")); \\ Vincenzo Librandi, Jan 28 2012 CROSSREFS Cf. A157373, A157374. Sequence in context: A356767 A112641 A203386 * A331659 A174746 A074906 Adjacent sequences: A157372 A157373 A157374 * A157376 A157377 A157378 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Feb 28 2009 STATUS approved

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Last modified December 3 09:50 EST 2022. Contains 358517 sequences. (Running on oeis4.)