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A157516 a(n) = 5000*n^2 - 200*n + 1. 3
4801, 19601, 44401, 79201, 124001, 178801, 243601, 318401, 403201, 498001, 602801, 717601, 842401, 977201, 1122001, 1276801, 1441601, 1616401, 1801201, 1996001, 2200801, 2415601, 2640401, 2875201, 3120001, 3374801, 3639601 (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 - A157514(n)*A157515(n)^2 = 1 (see also the second part of the comment at A157514). - Vincenzo Librandi, Jan 26 2012
LINKS
Vincenzo Librandi, X^2-AY^2=1
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 26 2012
G.f.: x*(-4801 - 5198*x - x^2)/(x-1)^3. - Vincenzo Librandi, Jan 26 2012
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {4801, 19601, 44401}, 50] (* Vincenzo Librandi, Jan 26 2012 *)
PROG
(Magma) I:=[4801, 19601, 44401]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jan 26 2012
(PARI) for(n=1, 22, print1(5000*n^2 - 200*n + 1", ")); \\ Vincenzo Librandi, Jan 26 2012
CROSSREFS
Sequence in context: A255412 A254791 A096790 * A157628 A214146 A085322
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 02 2009
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)