A157663 a(n) = 8000*n + 40.

8040, 16040, 24040, 32040, 40040, 48040, 56040, 64040, 72040, 80040, 88040, 96040, 104040, 112040, 120040, 128040, 136040, 144040, 152040, 160040, 168040, 176040, 184040, 192040, 200040, 208040, 216040, 224040, 232040, 240040, 248040, 256040

Offset: 1

Author

Vincenzo Librandi, Mar 04 2009

Keywords

• nonn
• easy

Comments

The identity (80000*n^2 + 800*n + 1)^2 - (100*n^2 + n)*(8000*n + 40)^2 = 1 can be written as A157664(n)^2 - A055438(n)*a(n)^2 = 1 (see Bruno Berselli's comment at A157664). - Vincenzo Librandi, Feb 04 2012

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).

Crossrefs

Cf. A055438, A157664.

Programs

GAP

List([1..40], n -> 40*(200*n + 1)); # G. C. Greubel, Nov 17 2018

Magma

I:=[8040, 16040]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 04 2012

Mathematica

LinearRecurrence[{2, -1}, {8040, 16040}, 50] (* Vincenzo Librandi, Feb 04 2012 *)
8000*Range[40]+40 (* Harvey P. Dale, Dec 31 2024 *)

PARI

for(n=1, 50, print1(8000*n + 40", ")); \\ Vincenzo Librandi, Feb 04 2012

Sage

[40*(200*n + 1) for n in (1..40)] # G. C. Greubel, Nov 17 2018

Formula

G.f.: x*(8040 - 40*x)/(1-x)^2. - Vincenzo Librandi, Feb 04 2012

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 04 2012

E.g.f.: 40*(-1 + (1 + 200*x)*exp(x)). - G. C. Greubel, Nov 17 2018