The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A173089 a(n) = 25*n^2 + n. 3
 26, 102, 228, 404, 630, 906, 1232, 1608, 2034, 2510, 3036, 3612, 4238, 4914, 5640, 6416, 7242, 8118, 9044, 10020, 11046, 12122, 13248, 14424, 15650, 16926, 18252, 19628, 21054, 22530, 24056, 25632, 27258, 28934, 30660, 32436, 34262, 36138, 38064, 40040, 42066, 44142, 46268, 48444, 50670, 52946, 55272, 57648 (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 A157511(n)^2 - a(n)*A157510(n)^2 = 1. This is the case s=5 of the identity (8*n^2*s^4 + 8*n*s^2 + 1)^2 -(n^2*s^2 + n)*(8*n*s^3 + 4*s)^2 = 1. - 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 G.f.: x*(-26 - 24*x)/(x-1)^3. - Vincenzo Librandi, Feb 04 2012 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 04 2012 MATHEMATICA LinearRecurrence[{3, -3, 1}, {26, 102, 228}, 50] (* Vincenzo Librandi, Feb 04 2012 *) PROG (MAGMA) [ 25*n^2+n: n in [1..50] ]; (PARI) for(n=1, 40, print1(25*n^2 + n", ")); \\ Vincenzo Librandi, Feb 04 2012 CROSSREFS Cf. A157510, A157511. Sequence in context: A136293 A065013 A031434 * A333055 A244633 A042320 Adjacent sequences:  A173086 A173087 A173088 * A173090 A173091 A173092 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Nov 22 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 8 19:29 EDT 2020. Contains 336298 sequences. (Running on oeis4.)