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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A158447 a(n) = 10*n^2 - 1. 2
9, 39, 89, 159, 249, 359, 489, 639, 809, 999, 1209, 1439, 1689, 1959, 2249, 2559, 2889, 3239, 3609, 3999, 4409, 4839, 5289, 5759, 6249, 6759, 7289, 7839, 8409, 8999, 9609, 10239, 10889, 11559, 12249, 12959, 13689, 14439, 15209, 15999, 16809, 17639 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (10*n^2-1)^2-(25*n.^2-5) *(2*n)^2=1 can be written as a(n)^2-A158446(n)*A005843(n)^2=1.

Sequence found by reading the line from 9, in the direction 9, 39,..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - Omar E. Pol, Jul 18 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Vincenzo Librandi, X^2-AY^2=1

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

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

G.f: x*(9+12*x-x^2)/(1-x)^3.

a(n) = A033583(n) - 1. - Omar E. Pol, Jul 18 2012

MAPLE

A158447:=n->10*n^2-1: seq(A158447(n), n=1..100); # Wesley Ivan Hurt, Apr 26 2017

MATHEMATICA

Table[10n^2-1, {n, 50}]

LinearRecurrence[{3, -3, 1}, {9, 39, 89}, 50] (* Harvey P. Dale, Dec 08 2017 *)

PROG

(MAGMA) I:=[9, 39, 89]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]];

(PARI) a(n) = 10*n^2 - 1.

CROSSREFS

Cf. A005843, A033583, A085787, A158446.

Sequence in context: A050854 A053181 A192608 * A281381 A226449 A299280

Adjacent sequences:  A158444 A158445 A158446 * A158448 A158449 A158450

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 19 2009

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 December 14 03:31 EST 2019. Contains 329978 sequences. (Running on oeis4.)