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 A157511 a(n) = 5000*n^2 + 200*n + 1. 3
 5201, 20401, 45601, 80801, 126001, 181201, 246401, 321601, 406801, 502001, 607201, 722401, 847601, 982801, 1128001, 1283201, 1448401, 1623601, 1808801, 2004001, 2209201, 2424401, 2649601, 2884801, 3130001, 3385201, 3650401 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The identity (5000*n^2 + 200*n + 1)^2 - (25*n^2 + n)*(1000*n + 20)^2 = 1 can be written as a(n)^2 - A173089(n)*A157510(n)^2 = 1 (see also second part of the comment at A173089). - Vincenzo Librandi, Feb 04 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 From Harvey P. Dale, May 24 2011: (Start) a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1)=5201, a(2)=20401, a(3)=45601. G.f.: -x*((5201 + x*(4798+x))/(x-1)^3). (End) MATHEMATICA Table[5000n^2+200n+1, {n, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {5201, 20401, 45601}, 40] (* Harvey P. Dale, May 24 2011 *) PROG (Magma) I:=[5201, 20401, 45601]; [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 04 2012 (PARI) for(n=1, 40, print1(5000*n^2 + 200*n + 1", ")); \\ Vincenzo Librandi, Feb 04 2012 CROSSREFS Cf. A157510, A173089. Sequence in context: A262909 A093071 A247266 * A165599 A109159 A231113 Adjacent sequences: A157508 A157509 A157510 * A157512 A157513 A157514 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Mar 02 2009 STATUS approved

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Last modified May 24 11:32 EDT 2024. Contains 372773 sequences. (Running on oeis4.)