A158224 a(n) = 196*n^2 - 2*n.

194, 780, 1758, 3128, 4890, 7044, 9590, 12528, 15858, 19580, 23694, 28200, 33098, 38388, 44070, 50144, 56610, 63468, 70718, 78360, 86394, 94820, 103638, 112848, 122450, 132444, 142830, 153608, 164778, 176340, 188294, 200640, 213378, 226508

Offset

1,1

Comments

The identity (196*n-1)^2-(196*n^2-2*n)*(14)^2=1 can be written as A158225(n)^2-a(n)*(14)^2=1.

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 15 in the first table at p. 85, case d(t) = t*(14^2*t-2)).

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).

G.f.: x*(-194-198*x)/(x-1)^3.

Maple

A158224:=n->196*n^2 - 2*n: seq(A158224(n), n=1..50); # Wesley Ivan Hurt, Jan 27 2017

Mathematica

Table[196n^2-2n, {n, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {194, 780, 1758}, 40] (* Harvey P. Dale, Jul 03 2017 *)

Prog

(PARI) a(n) = 196*n^2 - 2*n;

Crossrefs

Cf. A158225.

Sequence in context: A294595 A248549 A278123 * A205621 A205356 A281807

Adjacent sequences: A158221 A158222 A158223 * A158225 A158226 A158227

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 14 2009

Status

approved