login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A154295 a(n) = 81*n^2 - 90*n + 26. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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).

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

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 *)

PROG

(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

(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

CROSSREFS

Cf. A154262, A154266.

Sequence in context: A131083 A203597 A040652 * A277685 A072360 A205322

Adjacent sequences:  A154292 A154293 A154294 * A154296 A154297 A154298

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Jan 06 2009

EXTENSIONS

Corrected by Don Reble, Jun 16 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 25 13:50 EDT 2019. Contains 326324 sequences. (Running on oeis4.)