A157669 a(n) = 19683*n - 5967.

13716, 33399, 53082, 72765, 92448, 112131, 131814, 151497, 171180, 190863, 210546, 230229, 249912, 269595, 289278, 308961, 328644, 348327, 368010, 387693, 407376, 427059, 446742, 466425, 486108, 505791, 525474, 545157, 564840, 584523

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 A157670(n)^2 - A157668(n)* a(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 (2,-1).

Formula

a(n) = 2*a(n-1) - a(n-2).

G.f.: x*(13716+5967*x)/(x-1)^2.

E.g.f.: 27*(221 - (221 - 729*x)*exp(x)). - G. C. Greubel, Nov 17 2018

Mathematica

LinearRecurrence[{2, -1}, {13716, 33399}, 40]

Prog

(Magma) I:=[13716, 33399]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]];
(PARI) a(n) = 19683*n - 5967.
(Sage) [19683*n - 5967 for n in (1..40)] # G. C. Greubel, Nov 17 2018
(GAP) List([1..40], n -> 19683*n - 5967); # G. C. Greubel, Nov 17 2018

Crossrefs

Cf. A157668, A157670.

Sequence in context: A047827 A204369 A226020 * A236052 A178486 A236708

Adjacent sequences: A157666 A157667 A157668 * A157670 A157671 A157672

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 04 2009

Status

approved