A157734 a(n) = 441*n^2 - 394*n + 88.

135, 1064, 2875, 5568, 9143, 13600, 18939, 25160, 32263, 40248, 49115, 58864, 69495, 81008, 93403, 106680, 120839, 135880, 151803, 168608, 186295, 204864, 224315, 244648, 265863, 287960, 310939, 334800, 359543, 385168, 411675, 439064

Offset

1,1

Comments

The identity (388962*n^2 - 347508*n + 77617)^2 - (441*n^2 - 394*n + 88)*(18522*n - 8274)^2 = 1 can be written as A157736(n)^2 - a(n)*A157735(n)^2 = 1.

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

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

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

a(n) = (9*n - 4)*(49*n - 22). - Bruno Berselli, Apr 23 2018

Mathematica

LinearRecurrence[{3, -3, 1}, {135, 1064, 2875}, 40]

Prog

(Magma) I:=[135, 1064, 2875]; [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 - 394*n + 88.

Crossrefs

Cf. A157735, A157736.

Sequence in context: A336554 A238330 A358002 * A334128 A210102 A061073

Adjacent sequences: A157731 A157732 A157733 * A157735 A157736 A157737

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 05 2009

Status

approved