A154295 a(n) = 81*n^2 - 90*n + 26.

26, 17, 170, 485, 962, 1601, 2402, 3365, 4490, 5777, 7226, 8837, 10610, 12545, 14642, 16901, 19322, 21905, 24650, 27557, 30626, 33857, 37250, 40805, 44522, 48401, 52442, 56645, 61010, 65537, 70226, 75077, 80090, 85265, 90602, 96101, 101762

Offset: 0

Author

Vincenzo Librandi, Jan 06 2009

Keywords

• nonn
• easy

Comments

The identity (81*n^2 + 72*n + 17)^2 - (9*n^2 + 8*n + 2)*(27*n + 12)^2 = 1 can be written as a(n+1)^2 - A154262(n+1)*A154266(n)^2 = 1. - Vincenzo Librandi, Feb 03 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A154262, A154266.

Programs

Magma

I:=[26, 17, 170]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 03 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {26, 17, 170}, 40] (* Vincenzo Librandi, Feb 03 2012 *)
Table[81*n^2 - 90*n + 26,{n,0,25}] (* G. C. Greubel, Sep 10 2016 *)

PARI

for(n=0, 22, print1(81*n^2-90*n+26", ")); \\ Vincenzo Librandi, Feb 03 2012

PARI

x='x+O('x^99); Vec((26-61*x+197*x^2)/(1-x)^3) \\ Altug Alkan, Sep 10 2016

Formula

a(n) = A002522(|9n-5|). - R. J. Mathar, Jan 07 2009

G.f.: (26 - 61*x + 197*x^2)/(1 - x)^3. - Vincenzo Librandi, Feb 03 2012

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Feb 03 2012

E.g.f.: (26 - 9*x + 81*x^2)*exp(x). - G. C. Greubel, Sep 10 2016

Extensions

Corrected by Don Reble, Jun 16 2010