A154378 a(n) = 250*n - 10.

240, 490, 740, 990, 1240, 1490, 1740, 1990, 2240, 2490, 2740, 2990, 3240, 3490, 3740, 3990, 4240, 4490, 4740, 4990, 5240, 5490, 5740, 5990, 6240, 6490, 6740, 6990, 7240, 7490, 7740, 7990, 8240, 8490, 8740, 8990, 9240, 9490, 9740, 9990, 10240, 10490

Offset: 1

Author

Vincenzo Librandi, Jan 08 2009

Keywords

• nonn
• easy

Comments

The identity (1250*n^2 - 100*n + 1)^2 - (25*n^2 - 2*n)*(250*n - 10)^2 = 1 can be written as A154374(n)^2 - A154376(n)*a(n)^2 = 1 (see also the second comment in A154374). - Vincenzo Librandi, Jan 30 2012

Links

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

Crossrefs

Cf. A154374, A154376.

Programs

Mathematica

LinearRecurrence[{2, -1}, {240, 490}, 50] (* Vincenzo Librandi, Jan 30 2012 *)

PARI

a(n)=250*n-10 \\ Charles R Greathouse IV, Dec 27 2011

Formula

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 30 2012

G.f.: 10*x*(x + 24)/(1-x)^2. - Vincenzo Librandi, Jan 30 2012

E.g.f.: 10*( (25*x - 1)*exp(x) + 1). - G. C. Greubel, Sep 15 2016