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!)
A077413 Bisection (odd part) of Chebyshev sequence with Diophantine property. 6
2, 13, 76, 443, 2582, 15049, 87712, 511223, 2979626, 17366533, 101219572, 589950899, 3438485822, 20040964033, 116807298376, 680802826223, 3968009658962, 23127255127549, 134795521106332, 785645871510443, 4579079707956326, 26688832376227513, 155553914549408752 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

-8*a(n)^2 + b(n)^2 = 17, with the companion sequence b(n) = A077239(n).

The even part is A054488(n) with Diophantine companion A077240(n).

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (6,-1).

FORMULA

a(n) = 6*a(n-1) - a(n-2), a(-1)=-1, a(0)=2.

a(n) = 2*S(n, 6)+S(n-1, 6), with S(n, x) = U(n, x/2), Chebyshev polynomials of 2nd kind, A049310. S(n, 6) = A001109(n+1).

G.f.: (2+x)/(1-6*x+x^2).

a(n) = (((3-2*sqrt(2))^n*(-7+4*sqrt(2))+(3+2*sqrt(2))^n*(7+4*sqrt(2))))/(4*sqrt(2)). - Colin Barker, Oct 12 2015

EXAMPLE

8*a(1)^2 + 17 = 8*13^2+17 = 1369 = 37^2 = A077239(1)^2.

PROG

(PARI) Vec((2+x)/(1-6*x+x^2) + O(x^30)) \\ Colin Barker, Jun 16 2015

CROSSREFS

Cf. A077241 (even and odd parts).

Sequence in context: A161130 A192700 A007509 * A024199 A037523 A037732

Adjacent sequences:  A077410 A077411 A077412 * A077414 A077415 A077416

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 23 09:54 EST 2017. Contains 295116 sequences.