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A157670 a(n) = 531441*n^2 - 322218*n + 48842. 3
258065, 1530170, 3865157, 7263026, 11723777, 17247410, 23833925, 31483322, 40195601, 49970762, 60808805, 72709730, 85673537, 99700226, 114789797, 130942250, 148157585, 166435802, 185776901, 206180882, 227647745, 250177490 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (531441*n^2 - 322218*n + 48842)^2 - (729*n^2 - 442*n + 67)*(19683*n - 5967)^2 = 1 can be written as a(n)^2 - A157668(n)*A157669(n)^2 = 1.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

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

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*(258065 + 755975*x + 48842*x^2)/(1-x)^3.

E.g.f.: (48842 + 209223*x + 531441*x^2)*exp(x) - 48842. - G. C. Greubel, Nov 17 2018

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {258065, 1530170, 3865157}, 40]

PROG

(MAGMA) I:=[258065, 1530170, 3865157]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];

(PARI) a(n) = 531441*n^2 - 322218*n + 48842.

(Sage) [531441*n^2 - 322218*n + 48842 for n in (1..40)] # G. C. Greubel, Nov 17 2018

(GAP) List([1..40], n -> 531441*n^2 - 322218*n + 48842); # G. C. Greubel, Nov 17 2018

CROSSREFS

Cf. A157668, A157669.

Sequence in context: A251165 A065794 A206253 * A252921 A216204 A153980

Adjacent sequences:  A157667 A157668 A157669 * A157671 A157672 A157673

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 04 2009

STATUS

approved

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Last modified June 17 15:38 EDT 2021. Contains 345085 sequences. (Running on oeis4.)