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

 

Logo


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 - 13*x)/(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

E.g.f.: exp(7*x)*(2*cosh(4*sqrt(3)*x) - sqrt(3)*sinh(4*sqrt(3)*x)). - Franck Maminirina Ramaharo, Nov 12 2018

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 *)

PROG

(Maxima) (a[0]:2, a[1]:2, a[n] := 14*a[n - 1] - a[n-2], makelist(a[n], n, 0, 50)); /* Franck Maminirina Ramaharo, Nov 12 2018 */

CROSSREFS

a(n) = 2*A001570(n).

Bisection of A001075.

Cf. A028230.

Sequence in context: A301602 A120979 A032000 * A236286 A288208 A024577

Adjacent sequences:  A094344 A094345 A094346 * A094348 A094349 A094350

KEYWORD

nonn,easy,changed

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 13 23:57 EST 2018. Contains 317150 sequences. (Running on oeis4.)