A154360 a(n) = 250*n - 180.

-180, 70, 320, 570, 820, 1070, 1320, 1570, 1820, 2070, 2320, 2570, 2820, 3070, 3320, 3570, 3820, 4070, 4320, 4570, 4820, 5070, 5320, 5570, 5820, 6070, 6320, 6570, 6820, 7070, 7320, 7570, 7820, 8070, 8320, 8570, 8820, 9070, 9320, 9570, 9820, 10070, 10320

Offset: 0

Author

Vincenzo Librandi, Jan 08 2009

Keywords

• sign
• easy

Comments

The identity (1250*n^2 - 1800*n + 649)^2 - (25*n^2 - 36*n + 13)*(250*n - 180)^2 = 1 can be written as A154358(n)^2 - A154355(n)*a(n)^2 = 1. See also the third comment in A154357.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A154361, A154359, A154358, A154357, A154355.

Programs

Magma

[250*n-180: n in [0..50]]; // Bruno Berselli, Sep 15 2016

Mathematica

LinearRecurrence[{2, -1}, {-180, 70}, 50] (* Vincenzo Librandi, Feb 21 2012 *)

PARI

for(n=0, 50, print1(250n - 180", ")); \\ Vincenzo Librandi, Feb 21 2012

Formula

G.f.: -10*(18 - 43*x)/(1-x)^2. - Bruno Berselli, Dec 13 2011

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 21 2012

E.g.f.: 10*(-18 + 25*x)*exp(x). - G. C. Greubel, Sep 15 2016

Extensions

Offset changed and Librandi's comment rewritten by Bruno Berselli, Dec 13 2011