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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A154262 a(n) = 9*n^2 - 10*n + 3. 4
3, 2, 19, 54, 107, 178, 267, 374, 499, 642, 803, 982, 1179, 1394, 1627, 1878, 2147, 2434, 2739, 3062, 3403, 3762, 4139, 4534, 4947, 5378, 5827, 6294, 6779, 7282, 7803, 8342, 8899, 9474, 10067, 10678, 11307, 11954, 12619, 13302, 14003, 14722, 15459 (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 A154295(n+1)^2 - a(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

From Vincenzo Librandi, Feb 02 2012: (Start)

G.f.: (3 - 7*x + 22*x^2)/(1-x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {2, 19, 54}, 50] (* Vincenzo Librandi, Feb 02 2012 *)

PROG

(PARI) a(n)=9*n^2-10*n+3 \\ Charles R Greathouse IV, Dec 27 2011

(MAGMA) I:=[2, 19, 54]; [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 02 2012

CROSSREFS

Cf. A154266, A154295.

Sequence in context: A094554 A223881 A206582 * A154261 A098655 A065038

Adjacent sequences:  A154259 A154260 A154261 * A154263 A154264 A154265

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Jan 06 2009

EXTENSIONS

Edited by Charles R Greathouse IV, Jul 25 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 October 17 11:26 EDT 2019. Contains 328108 sequences. (Running on oeis4.)