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!)
A028563 a(n) = n*(n+7). 21
0, 8, 18, 30, 44, 60, 78, 98, 120, 144, 170, 198, 228, 260, 294, 330, 368, 408, 450, 494, 540, 588, 638, 690, 744, 800, 858, 918, 980, 1044, 1110, 1178, 1248, 1320, 1394, 1470, 1548, 1628, 1710, 1794, 1880, 1968, 2058, 2150, 2244, 2340, 2438, 2538, 2640, 2744, 2850, 2958, 3068, 3180, 3294 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(m), for m >= 1, are the only positive integer values of t for which the Binet-de Moivre formula of the recurrence b(n) = 7*b(n-1)+t*b(n-2) has a square root whose radicand is a square. In particular, sqrt(7^2+4*t) is a positive integer since 7^2+4*t = 7^2+4*a(m) = (2*m+7)^2. Thus the characteristic roots are r1 = 7+m and r2 = -m. - Felix P. Muga II, Mar 28 2014 (edited - Wolfdieter Lang, Apr 17 2014)

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Patrick De Geest, Palindromic Quasipronics of the form n(n+x).

Felix P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, Preprint on ResearchGate, March 2014.

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

FORMULA

Equals 2*A055999. - Zerinvary Lajos, Feb 12 2007

a(n) = 2*n+a(n-1)+6. - Vincenzo Librandi, Aug 05 2010

Sum_{n>=1} 1/a(n) = 363/980 = 0.37040816... - R. J. Mathar, Mar 22 2011

G.f.: 2*x*(4-3*x)/(1-x)^3. - Colin Barker, Feb 17 2012

Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/7 - 319/2940. - Amiram Eldar, Jan 15 2021

MAPLE

A028563:=n->n*(n + 7); seq(A028563(n), n=0..50); # Wesley Ivan Hurt, Mar 30 2014

MATHEMATICA

CoefficientList[Series[2 x (4 - 3 x)/(1 - x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Oct 18 2013 *)

LinearRecurrence[{3, -3, 1}, {0, 8, 18}, 60] (* Harvey P. Dale, Oct 07 2015 *)

PROG

(Magma) [n*(n+7): n in [0..60]]; // Vincenzo Librandi, Oct 18 2013

(PARI) a(n)=n*(n+7) \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. A002522, A055999.

Sequence in context: A278546 A092163 A100592 * A171523 A120091 A211526

Adjacent sequences: A028560 A028561 A028562 * A028564 A028565 A028566

KEYWORD

nonn,easy

AUTHOR

Patrick De Geest

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 5 14:51 EST 2022. Contains 358588 sequences. (Running on oeis4.)