A154379 a(n) = 250*n + 10.

260, 510, 760, 1010, 1260, 1510, 1760, 2010, 2260, 2510, 2760, 3010, 3260, 3510, 3760, 4010, 4260, 4510, 4760, 5010, 5260, 5510, 5760, 6010, 6260, 6510, 6760, 7010, 7260, 7510, 7760, 8010, 8260, 8510, 8760, 9010, 9260, 9510, 9760, 10010, 10260

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 A154375(n)^2 - A154377(n)*a(n)^2 = 1 (see also the second comment in A154375). - 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. A154375, A154377.

Programs

Mathematica

LinearRecurrence[{2, -1}, {260, 510}, 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*(26 - x)/(1-x)^2. - Vincenzo Librandi, Jan 30 2012 [corrected by Georg Fischer, May 12 2019]

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

Extensions

Definition corrected by Paolo P. Lava, Jan 14 2009