A154375 a(n) = 1250*n^2 + 100*n + 1.

1351, 5201, 11551, 20401, 31751, 45601, 61951, 80801, 102151, 126001, 152351, 181201, 212551, 246401, 282751, 321601, 362951, 406801, 453151, 502001, 553351, 607201, 663551, 722401, 783751, 847601, 913951, 982801, 1054151, 1128001

Offset

1,1

Comments

The identity (1250*n^2 + 100*n + 1)^2 - (25*n^2 + 2*n)*(250*n + 10)^2 = 1 can be written as a(n)^2 - A154377(n)*A154379(n)^2 = 1. - Vincenzo Librandi, Jan 30 2012

This is the case s=5 of the identity (2*s^4*n^2 + 4*s^2*n + 1)^2 - (s^2*n^2 + 2*n)*(2*s^3*n + 2*s)^2 = 1. - Bruno Berselli, Jan 30 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(1)=1351, a(2)=5201, a(3)=11551, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Apr 25 2011

G.f.: x*(x^2 + 1148*x + 1351)/(1-x)^3. - Vincenzo Librandi, Jan 30 2012

E.g.f.: (1250*x^2 + 1350*x + 1)*exp(x) - 1. - G. C. Greubel, Sep 15 2016

Mathematica

Table[1250n^2+100n+1, {n, 30}] (* or *) LinearRecurrence[{3, -3, 1}, {1351, 5201, 11551}, 30] (* Harvey P. Dale, Apr 25 2011 *)

Prog

(PARI)  a(n)=1250*n^2+100*n+1 \\ Charles R Greathouse IV, Dec 27 2011

Crossrefs

Cf. A154377, A154379.

Sequence in context: A307218 A278383 A174638 * A243132 A349070 A035889

Adjacent sequences: A154372 A154373 A154374 * A154376 A154377 A154378

Keyword

nonn,easy

Author

Vincenzo Librandi, Jan 08 2009

Extensions

Minor corrections by M. F. Hasler, Oct 08 2014

Status

approved