login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A158482 a(n) = 14*n^2 + 1. 5
15, 57, 127, 225, 351, 505, 687, 897, 1135, 1401, 1695, 2017, 2367, 2745, 3151, 3585, 4047, 4537, 5055, 5601, 6175, 6777, 7407, 8065, 8751, 9465, 10207, 10977, 11775, 12601, 13455, 14337, 15247, 16185, 17151, 18145, 19167, 20217, 21295, 22401 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (14*n^2+1)^2-(49*n^2+7)*(2*n)^2=1 can be written as a(n)^2-A158481(n)*A005843(n)^2=1.

Sequence found by reading the line from 15, in the direction 15, 57,..., in the square spiral whose vertices are the generalized enneagonal numbers numbers A118277. Also sequence found by reading the same line in the square spiral whose edges have length A195019 and whose vertices are the numbers A195020. - Omar E. Pol, Sep 13 2011

LINKS

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

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*(15+12*x+x^2)/(1-x)^3.

From Amiram Eldar, Feb 05 2021: (Start)

Sum_{n>=0} 1/a(n) = (1 - (Pi/sqrt(14))*coth(Pi/sqrt(14)))/2.

Sum_{n>=0} (-1)^n/a(n) = (1 + (Pi/sqrt(14))*csch(Pi/sqrt(14)))/2.

Product_{n>=0} (1 + 1/a(n)) = sqrt(2)*csch(Pi/sqrt(14))*sinh(Pi/sqrt(7)).

Product_{n>=1} (1 - 1/a(n)) = (Pi/sqrt(14))*csch(Pi/sqrt(14)). (End)

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {15, 57, 127}, 50]

PROG

(Magma) I:=[15, 57, 127]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];

(PARI) a(n) = 14*n^2+1;

CROSSREFS

Cf. A005843, A158481.

Sequence in context: A020222 A256867 A336251 * A184223 A084815 A240152

Adjacent sequences: A158479 A158480 A158481 * A158483 A158484 A158485

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 20 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 3 09:50 EST 2022. Contains 358517 sequences. (Running on oeis4.)