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!)
A077243 Bisection (odd part) of Chebyshev sequence with Diophantine property. 4
2, 17, 134, 1055, 8306, 65393, 514838, 4053311, 31911650, 251239889, 1978007462, 15572819807, 122604550994, 965263588145, 7599504154166, 59830769645183, 471046653007298, 3708542454413201, 29197292982298310 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

-5*a(n)^2 + 3* b(n)^2 = 7, with the companion sequence b(n)= A077244(n).

The even part is A077245(n) with Diophantine companion A077246(n).

LINKS

Table of n, a(n) for n=0..18.

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (8,-1).

FORMULA

a(n)= 8*a(n-1) - a(n-2), a(-1)=-1, a(0)=2.

a(n)= 2*S(n, 8)+S(n-1, 8), with S(n, x) := U(n, x/2), Chebyshev polynomials of 2nd kind, A049310. S(n, 8)= A001090(n+1).

G.f.: (2+x)/(1-8*x+x^2).

a(n)=[4-sqrt(15)]^n-(3/10)*[4-sqrt(15)]^n*sqrt(15)+[4+sqrt(15)]^n+(3/10)*sqrt(15)*[4 +sqrt(15)]^n, with n>=0 - Paolo P. Lava, Jul 08 2008

EXAMPLE

5*a(1)^2 + 7 = 5*17^2+7 = 1452 = 3*22^2 = 3*A077244(1)^2.

MATHEMATICA

LinearRecurrence[{8, -1}, {2, 17}, 30] (* Harvey P. Dale, Oct 03 2015 *)

CROSSREFS

Sequence in context: A007354 A180840 A261120 * A037525 A037734 A201782

Adjacent sequences:  A077240 A077241 A077242 * A077244 A077245 A077246

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Nov 08 2002

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 22 15:27 EST 2017. Contains 295089 sequences.