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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

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Last modified August 20 17:05 EDT 2017. Contains 290836 sequences.