A156844 279841n^2 - 394634n + 139128.

24335, 469224, 1473795, 3038048, 5161983, 7845600, 11088899, 14891880, 19254543, 24176888, 29658915, 35700624, 42302015, 49463088, 57183843, 65464280, 74304399, 83704200, 93663683, 104182848, 115261695, 126900224

Offset

1,1

Comments

The identity (279841*n^2-394634*n+139128)^2-(529*n^2-746*n+263)*(12167*n-8579)^2=1 can be written as a(n)^2-A156842(n)*A156845(n)^2=1.

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

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

G.f.: x*(-24335-396219*x-139128*x^2)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {24335, 469224, 1473795}, 40]
Table[279841n^2-394634n+139128, {n, 30}] (* Harvey P. Dale, Mar 02 2021 *)

Prog

(Magma) I:=[24335, 469224, 1473795]; [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)=279841*n^2-394634*n+139128 \\ Charles R Greathouse IV, Dec 23 2011

Crossrefs

CF. A156842, A156845, A156849.

Sequence in context: A294856 A025041 A156843 * A174754 A206682 A083621

Adjacent sequences: A156841 A156842 A156843 * A156845 A156846 A156847

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 17 2009

Extensions

Edited by Charles R Greathouse IV, Jul 25 2010

Status

approved