A157653 a(n) = 80000*n^2 - 39200*n + 4801.

45601, 246401, 607201, 1128001, 1808801, 2649601, 3650401, 4811201, 6132001, 7612801, 9253601, 11054401, 13015201, 15136001, 17416801, 19857601, 22458401, 25219201, 28140001, 31220801, 34461601, 37862401, 41423201, 45144001

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 a(n)^2 - A157651(n)*A157652(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 (3,-3,1).

Formula

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

G.f.: x*(45601 + 109598*x + 4801*x^2)/(1-x)^3.

E.g.f.: (4801 + 40800*x + 80000*x^2)*exp(x) - 4801. - G. C. Greubel, Nov 17 2018

Mathematica

LinearRecurrence[{3, -3, 1}, {45601, 246401, 607201}, 40]

Prog

(Magma) I:=[45601, 246401, 607201]; [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) = 80000*n^2 - 39200*n + 4801.
(Sage) [80000*n^2-39200*n+4801 for n in (1..40)] # G. C. Greubel, Nov 17 2018
(GAP) List([1..40], n -> 80000*n^2-39200*n+4801); # G. C. Greubel, Nov 17 2018

Crossrefs

Cf. A157651, A157652.

Sequence in context: A253045 A251397 A184473 * A202915 A257358 A232255

Adjacent sequences: A157650 A157651 A157652 * A157654 A157655 A157656

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 03 2009

Status

approved