A157948 a(n) = 64*n^2 - n.

63, 254, 573, 1020, 1595, 2298, 3129, 4088, 5175, 6390, 7733, 9204, 10803, 12530, 14385, 16368, 18479, 20718, 23085, 25580, 28203, 30954, 33833, 36840, 39975, 43238, 46629, 50148, 53795, 57570, 61473, 65504, 69663, 73950, 78365, 82908

Offset

1,1

Comments

The identity (128*n - 1)^2 - (64*n^2 - n)*16^2 = 1 can be written as A157949(n)^2 - a(n)*16^2 = 1. - Vincenzo Librandi, Jan 29 2012

Links

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

Vincenzo Librandi, X^2-AY^2=1

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*(8^2*t-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 29 2012

G.f.: x*(-63-65*x)/(x-1)^3. - Vincenzo Librandi, Jan 29 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {63, 254, 573}, 50] (* Vincenzo Librandi, Jan 29 2012 *)
Table[64n^2-n, {n, 40}] (* Harvey P. Dale, May 30 2017 *)

Prog

(Magma) I:=[63, 254, 573]; [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 29 2012
(PARI) for(n=1, 40, print1(64*n^2 - n", ")); \\ Vincenzo Librandi, Jan 29 2012

Crossrefs

Cf. A157949.

Sequence in context: A184457 A184449 A158676 * A326388 A158684 A063398

Adjacent sequences: A157945 A157946 A157947 * A157949 A157950 A157951

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 10 2009

Status

approved