A154374 a(n) = 1250*n^2 - 100*n + 1.

1151, 4801, 10951, 19601, 30751, 44401, 60551, 79201, 100351, 124001, 150151, 178801, 209951, 243601, 279751, 318401, 359551, 403201, 449351, 498001, 549151, 602801, 658951, 717601, 778751, 842401, 908551, 977201, 1048351, 1122001

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 a(n)^2 - A154376(n)*A154378(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).

Crossrefs

Cf. A154376, A154378.

Programs

Magma

I:=[1151, 4801, 10951]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jan 30 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {1151, 4801, 10951}, 40] (* Vincenzo Librandi, Jan 30 2012 *)

PARI

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

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 29 2012

G.f.: x*(1151 + 1348*x + x^2)/(1-x)^3. - Vincenzo Librandi, Jan 29 2012

E.g.f.: -1 + (1 + 1150*x + 1250*x^2)*exp(x). - G. C. Greubel, Sep 15 2016