login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A132594 Values X satisfying the equation: X(X + 1) - 7*Y^2 = 0. 0
0, 63, 16128, 4096575, 1040514048, 264286471743, 67127723308800, 17050177433963583, 4330677940503441408, 1099975146710440154175, 279389356586511295719168, 70963796597827158672514623 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The full set of integer solutions to this equation consists of the pairs [X(i),Y(i)] = [1+-A001081(i), Y(i)=A001080(i)]. The present generates every second one of them: a(n) = [A001081(2n)-1]/2. - R. J. Mathar, Nov 20 2007

LINKS

Table of n, a(n) for n=0..11.

Index entries for linear recurrences with constant coefficients, signature (255, -255, 1).

FORMULA

a(0)=0, a(1)=63 and a(n)=254*a(n-1) - a(n-2) + 126.

G.f.: -63*x*(1+x)/(-1+x)/(1-254*x+x^2). a(n) = [A001081(2n)-1]/2. - R. J. Mathar, Nov 20 2007

a(n)=-(1/2)+(1/4)*[127-48*sqrt(7)]^n+(1/4)*[127+48*sqrt(7)]^n, with n>=0 [From Paolo P. Lava, Sep 26 2008]

a(0)=0, a(1)=63, a(2)=16128, a(n)=255*a(n-1)-255*a(n-2)+a(n-3). - Harvey P. Dale, Dec 15 2012

MATHEMATICA

LinearRecurrence[{255, -255, 1}, {0, 63, 16128}, 20] (* Harvey P. Dale, Dec 15 2012 *)

CROSSREFS

Cf. A007654.

Cf. A001080, A001081.

Sequence in context: A270507 A289875 A062208 * A212932 A177233 A183482

Adjacent sequences:  A132591 A132592 A132593 * A132595 A132596 A132597

KEYWORD

nonn

AUTHOR

Mohamed Bouhamida, Nov 14 2007

EXTENSIONS

More terms from Max Alekseyev, Nov 13 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 5 10:47 EDT 2020. Contains 334840 sequences. (Running on oeis4.)