A157373 a(n) = 49*n^2 - 20*n + 2.

31, 158, 383, 706, 1127, 1646, 2263, 2978, 3791, 4702, 5711, 6818, 8023, 9326, 10727, 12226, 13823, 15518, 17311, 19202, 21191, 23278, 25463, 27746, 30127, 32606, 35183, 37858, 40631, 43502, 46471, 49538, 52703, 55966, 59327, 62786, 66343

Offset

1,1

Comments

The identity (2401*n^2-980*n+99)^2-(49*n^2-20*n +2)*(343*n-70)^2=1 can be written as A157375(n)^2-a(n)*A157374(n)^2=1. - Vincenzo Librandi, Jan 28 2012

The continued fraction expansion of sqrt(a(n)) is [7n-2; {1, 1, 3, 7n-2, 3, 1, 1, 14n-4}]. - Magus K. Chu, Sep 06 2022

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) = 49*n^2-20*n+2.

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3), with a(1)=31, a(2)=158, a(3)=383. - Harvey P. Dale, Jun 20 2011

G.f.: x*(-31-65*x-2*x^2)/(x-1)^3. - Harvey P. Dale, Jun 20 2011

E.g.f.: (49*x^2 + 29*x + 2)*exp(x) - 2. - G. C. Greubel, Feb 02 2018

Mathematica

Table[49n^2-20n+2, {n, 40}](* Harvey P. Dale, Apr 01 2011 *)
LinearRecurrence[{3, -3, 1}, {31, 158, 383}, 40] (* or *) CoefficientList[ Series[ (-31-65x-2x^2)/(x-1)^3, {x, 0, 40}], x] (* Harvey P. Dale, Jun 20 2011 *)

Prog

(PARI) a(n)=49*n^2-20*n+2 \\ Charles R Greathouse IV, Jun 20 2011
(Magma) I:=[31, 158, 383]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jan 28 2012

Crossrefs

Cf. A157374, A157375.

Sequence in context: A042882 A045160 A142906 * A058285 A372931 A268258

Adjacent sequences: A157370 A157371 A157372 * A157374 A157375 A157376

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 28 2009

Status

approved