A157730 a(n) = 441*n^2 - 488*n + 135.

88, 923, 2640, 5239, 8720, 13083, 18328, 24455, 31464, 39355, 48128, 57783, 68320, 79739, 92040, 105223, 119288, 134235, 150064, 166775, 184368, 202843, 222200, 242439, 263560, 285563, 308448, 332215, 356864, 382395, 408808, 436103, 464280

Offset

1,1

Comments

The identity (388962*n^2 - 430416*n + 119071)^2 - (441*n^2 - 488*n + 135)*(18522*n - 10248)^2 = 1 can be written as A157732(n)^2 - a(n)*A157731(n)^2 = 1.

441*a(n) + 1 is a square. - Bruno Berselli, Apr 23 2018

The continued fraction expansion of sqrt(a(n)) is [21n-12; {2, 1, 1, 1, 2, 41n-24}]. - Magus K. Chu, Sep 23 2022

Links

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

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

G.f.: x*(88 + 659*x + 135*x^2)/(1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

a(n) = (9*n - 5)*(49*n - 27). - Bruno Berselli, Apr 23 2018

Mathematica

LinearRecurrence[{3, -3, 1}, {88, 923, 2640}, 40]

Prog

(Magma) I:=[88, 923, 2640]; [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) = 441*n^2 - 488*n + 135.

Crossrefs

Cf. A157731, A157732.

Sequence in context: A136933 A136958 A137049 * A055749 A227479 A321061

Adjacent sequences: A157727 A157728 A157729 * A157731 A157732 A157733

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 05 2009

Status

approved