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A158325 a(n) = 484n^2 + 2n. 2
486, 1940, 4362, 7752, 12110, 17436, 23730, 30992, 39222, 48420, 58586, 69720, 81822, 94892, 108930, 123936, 139910, 156852, 174762, 193640, 213486, 234300, 256082, 278832, 302550, 327236, 352890, 379512, 407102, 435660, 465186, 495680 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (484*n+1)^2 - (484*n^2 + 2*n)*(22)^2 = 1 can be written as A158326(n)^2 - a(n)*(22)^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*(22^2*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*(486+482*x)/(1-x)^3.

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {486, 1940, 4362}, 50]

PROG

(MAGMA) I:=[486, 1940, 4362]; [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) = 484*n^2 + 2*n.

CROSSREFS

Cf. A158326.

Sequence in context: A235525 A249227 A130181 * A187860 A205240 A206146

Adjacent sequences:  A158322 A158323 A158324 * A158326 A158327 A158328

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 16 2009

STATUS

approved

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Last modified March 30 21:56 EDT 2020. Contains 333132 sequences. (Running on oeis4.)