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

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A094347 a(n) = 14*a(n-1)-a(n-2); a(0) = a(1) = 2. 6
2, 2, 26, 362, 5042, 70226, 978122, 13623482, 189750626, 2642885282, 36810643322, 512706121226, 7141075053842, 99462344632562, 1385331749802026, 19295182152595802, 268747218386539202, 3743165875258953026 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Even x satisfying the Pellian x^2 - 3*y^2 = 1. For corresponding y see A028230.

LINKS

Table of n, a(n) for n=0..17.

R. K. Guy, Letter to N. J. A. Sloane concerning A001075, A011943, A094347 [Scanned and annotated letter, included with permission]

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (14,-1).

FORMULA

G.f.: 2*(1-13x)/(1-14*x+x^2). [Philippe Deléham, Nov 17 2008]

a(n) = ( (2+sqrt(3))^(2*n-1) + (2-sqrt(3))^(2*n-1) )/2. - Gerry Martens, Jun 03 2015

a(n) = (1/2)*sqrt(4+(-2*sqrt(-2+(7-4*sqrt(3))^(2*n)+(7+4*sqrt(3))^(2*n))+sqrt(3)*sqrt(2+(7-4*sqrt(3))^(2*n)+(7+4*sqrt(3))^(2*n)))^2). - Gerry Martens, Jun 03 2015

MATHEMATICA

LinearRecurrence[{14, -1}, {2, 2}, 40] (* or *) CoefficientList[ Series[2(1-13x)/(1-14x+x^2), {x, 0, 39}], x] (* Harvey P. Dale, Apr 23 2011 *)

CROSSREFS

a(n) = 2*A001570(n). Bisection of A001075. Cf. A028230.

Sequence in context: A195967 A120979 A032000 * A236286 A288208 A024577

Adjacent sequences:  A094344 A094345 A094346 * A094348 A094349 A094350

KEYWORD

nonn,easy

AUTHOR

Lekraj Beedassy, Jun 03 2004

EXTENSIONS

Corrected by Lekraj Beedassy, Jun 11 2004

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 21 22:32 EST 2017. Contains 295054 sequences.