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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
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, 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)).
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
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 16 2009
STATUS
approved