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
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Feb 28 2009
STATUS
approved