A154361 a(n) = 250*n - 70.

-70, 180, 430, 680, 930, 1180, 1430, 1680, 1930, 2180, 2430, 2680, 2930, 3180, 3430, 3680, 3930, 4180, 4430, 4680, 4930, 5180, 5430, 5680, 5930, 6180, 6430, 6680, 6930, 7180, 7430, 7680, 7930, 8180, 8430, 8680, 8930, 9180

Offset: 0

Author

Vincenzo Librandi, Jan 08 2009

Keywords

• sign
• easy

Comments

The identity (1250*n^2 - 700*n + 99)^2 - (25*n^2 - 14*n + 2)*(250*n - 70)^2 = 1 can be written as A154359(n)^2 - A154357(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. A154360, A154359, A154358, A154357, A154355.

Programs

Magma

[250*n-70: n in [0..50]]; // Bruno Berselli, Sep 15 2016

Mathematica

LinearRecurrence[{2, -1}, {-70, 180}, 50] (* Vincenzo Librandi, Feb 21 2012 *)
250*Range[0,50]-70 (* Harvey P. Dale, Apr 09 2020 *)

PARI

for(n=0, 50, print1(250*n - 70", ")); \\ Vincenzo Librandi, Feb 21 2012

Formula

G.f.: -10*(7 - 32*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*(-7 + 25*x)*exp(x). - G. C. Greubel, Sep 15 2016

Extensions

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