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A157665 a(n) = 729*n^2 - 1016*n + 354. 3
67, 1238, 3867, 7954, 13499, 20502, 28963, 38882, 50259, 63094, 77387, 93138, 110347, 129014, 149139, 170722, 193763, 218262, 244219, 271634, 300507, 330838, 362627, 395874, 430579, 466742, 504363, 543442, 583979, 625974, 669427, 714338 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (531441*n^2 - 740664*n + 258065)^2 - (729*n^2 - 1016*n + 354)*(19683*n - 13716)^2 = 1 can be written as A157667(n)^2 - a(n)*A157666(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*(67 + 1037*x + 354*x^2)/(1-x)^3.

E.g.f.: (1 - 287*x + 729*x^2)*exp(x) - 354. - G. C. Greubel, Nov 17 2018

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {67, 1238, 3867}, 40]

PROG

(MAGMA) I:=[67, 1238, 3867]; [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) = 729*n^2 - 1016*n + 354.

(Sage) [729*n^2 - 1016*n + 354 for n in (1..40)] # G. C. Greubel, Nov 17 2018

(GAP) List([1..40], n -> 729*n^2 - 1016*n + 354); # G. C. Greubel, Nov 17 2018

CROSSREFS

Cf. A157666, A157667.

Sequence in context: A093267 A032651 A322880 * A231193 A078850 A092795

Adjacent sequences:  A157662 A157663 A157664 * A157666 A157667 A157668

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 04 2009

STATUS

approved

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Last modified August 10 02:28 EDT 2020. Contains 336367 sequences. (Running on oeis4.)