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A158692 a(n)=33*(33*n^2-1). 1
1056, 4323, 9768, 17391, 27192, 39171, 53328, 69663, 88176, 108867, 131736, 156783, 184008, 213411, 244992, 278751, 314688, 352803, 393096, 435567, 480216, 527043, 576048, 627231, 680592, 736131, 793848, 853743, 915816, 980067, 1046496 (list; graph; refs; listen; history; internal format)
OFFSET

1,1

COMMENTS

The identity (66*n^2-1)^2 - (1089*n^2-33) * (2*n)^2 = 1 can be written as

the Pell equation (A158693(n))^2 - a(n) * (A005843(n))^2 = 1.

LINKS

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

Edward Everett Withford, Pell Equation

Wolfram MathWorld, Pell Equation

FORMULA

a(n)= 3*a(n-1) -3*a(n-2) +a(n-3). G.f.: 33*x*(-32-35*x+x^2)/(x-1)^3.

CROSSREFS

Cf. A005843, A158693

Sequence in context: A185680 A191858 A090005 * A023072 A168627 A035858

Adjacent sequences:  A158689 A158690 A158691 * A158693 A158694 A158695

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 24 2009

EXTENSIONS

Comment rewritten and formula replaced by R. J. Mathar, (mathar(AT)strw.leidenuniv.nl), Oct 22 2009

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Last modified February 14 10:43 EST 2012. Contains 205614 sequences.