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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 A024577 A121222

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

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Last modified May 30 04:27 EDT 2017. Contains 287305 sequences.