A157652 a(n) = 40*(200*n - 49).

6040, 14040, 22040, 30040, 38040, 46040, 54040, 62040, 70040, 78040, 86040, 94040, 102040, 110040, 118040, 126040, 134040, 142040, 150040, 158040, 166040, 174040, 182040, 190040, 198040, 206040, 214040, 222040, 230040, 238040, 246040, 254040

Offset

1,1

Comments

The identity (80000*n^2 -39200*n +4801)^2 - (100*n^2 -49*n +6)*(8000*n -1960)^2 = 1 can be written as A157653(n)^2 - A157651(n)*a(n)^2 = 1.

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 (2,-1).

Formula

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

G.f.: x*(6040+1960*x)/(x-1)^2.

E.g.f.: 40*(49 - (49 - 200*x)*exp(x)). - G. C. Greubel, Nov 17 2018

Mathematica

LinearRecurrence[{2, -1}, {6040, 14040}, 40]

Prog

(Magma) I:=[6040, 14040]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]];
(PARI) a(n) = 8000*n - 1960.
(Sage) [40*(200*n - 49) for n in (1..40)] # G. C. Greubel, Nov 17 2018
(GAP) List([1..40], n -> 40*(200*n - 49)); # G. C. Greubel, Nov 17 2018

Crossrefs

Cf. A157651, A157653.

Sequence in context: A203352 A064248 A202895 * A264949 A237961 A362954

Adjacent sequences: A157649 A157650 A157651 * A157653 A157654 A157655

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 03 2009

Status

approved