A157947 a(n) = 98n + 1.

99, 197, 295, 393, 491, 589, 687, 785, 883, 981, 1079, 1177, 1275, 1373, 1471, 1569, 1667, 1765, 1863, 1961, 2059, 2157, 2255, 2353, 2451, 2549, 2647, 2745, 2843, 2941, 3039, 3137, 3235, 3333, 3431, 3529, 3627, 3725, 3823, 3921, 4019, 4117, 4215, 4313

Offset

1,1

Comments

The identity (98*n+1)^2 - (49*n^2 + n)*14^2 = 1 can be written as a(n)^2 - A173141(n)*14^2 = 1. - Vincenzo Librandi, Feb 10 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 14 in the first table at p. 85, case d(t) = t*(7^2*t+1)).

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 10 2012

G.f.: x*(99-x)/(1-x)^2. - Vincenzo Librandi, Feb 10 2012

Mathematica

LinearRecurrence[{2, -1}, {99, 197}, 50] (* Vincenzo Librandi, Feb 10 2012 *)
98*Range[50]+1 (* Harvey P. Dale, Mar 23 2012 *)

Prog

(Magma) I:=[99, 197]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 10 2012
(PARI) for(n=1, 50, print1(98n + 1", ")); \\ Vincenzo Librandi, Feb 10 2012

Crossrefs

Cf. A173141.

Sequence in context: A075814 A320707 A235228 * A097599 A033674 A043526

Adjacent sequences: A157944 A157945 A157946 * A157948 A157949 A157950

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 10 2009

Status

approved