A158222 a(n) = 196*n^2 + 2*n.

198, 788, 1770, 3144, 4910, 7068, 9618, 12560, 15894, 19620, 23738, 28248, 33150, 38444, 44130, 50208, 56678, 63540, 70794, 78440, 86478, 94908, 103730, 112944, 122550, 132548, 142938, 153720, 164894, 176460, 188418, 200768, 213510, 226644

Offset

1,1

Comments

The identity (196*n+1)^2-(196*n^2+2*n)*(14)^2=1 can be written as A158223(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*x-198)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {198, 788, 1770}, 50]
Table[196n^2+2n, {n, 50}] (* Harvey P. Dale, Jul 10 2021 *)

Prog

(Magma) I:=[198, 788, 1770]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];
(PARI) a(n) = 196*n^2+2*n.

Crossrefs

Cf. A158223.

Sequence in context: A357076 A252952 A252945 * A156771 A065697 A159204

Adjacent sequences: A158219 A158220 A158221 * A158223 A158224 A158225

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 14 2009

Status

approved