A154359 a(n) = 1250*n^2 - 700*n + 99.

99, 649, 3699, 9249, 17299, 27849, 40899, 56449, 74499, 95049, 118099, 143649, 171699, 202249, 235299, 270849, 308899, 349449, 392499, 438049, 486099, 536649, 589699, 645249, 703299, 763849, 826899, 892449, 960499, 1031049

Offset: 0

Author

Vincenzo Librandi, Jan 08 2009

Keywords

• nonn
• 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 a(n)^2 - A154357(n)*A154361(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 (3,-3,1).

Programs

Magma

[1250*n^2-700*n+99: n in [0..40]]; // Bruno Berselli, Sep 15 2016

Mathematica

LinearRecurrence[{3, -3, 1}, {99, 649, 3699}, 50] (* Vincenzo Librandi, Feb 21 2012 *)

PARI

for(n=0, 40, print1(1250*n^2-700*n+99", ")); \\ Vincenzo Librandi, Feb 21 2012

Formula

G.f.: (99 + 352*x + 2049*x^2)/(1-x)^3. - Bruno Berselli, Dec 13 2011

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Feb 21 2012

E.g.f.: (99 + 550*x + 1250*x^2)*exp(x). - G. C. Greubel, Sep 15 2016

Extensions

Edited by Charles R Greathouse IV, Jul 29 2010

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