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A077245 Bisection (even part) of Chebyshev sequence with Diophantine property. 4
1, 10, 79, 622, 4897, 38554, 303535, 2389726, 18814273, 148124458, 1166181391, 9181326670, 72284431969, 569094129082, 4480468600687, 35274654676414, 277716768810625, 2186459495808586, 17213959197658063 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

3*b(n)^2 - 5*a(n)^2 = 7, with the companion sequence b(n)= A077246(n).

The odd part is A077243(n) with Diophantine companion A077244(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) := -2, a(0)=1.

a(n)= S(n, 8)+2*S(n-1, 8), with S(n, x) := U(n, x/2), Chebyshev's polynomials of the 2nd kind, A049310. S(-1, x) := 0 and S(n, 8)= A001090(n+1).

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

a(n)=(1/2)*[4-sqrt(15)]^n-(1/5)*[4-sqrt(15)]^n*sqrt(15)+(1/2)*[4+sqrt(15)]^n+(1/5)*sqrt(15) *[4+sqrt(15)]^n, with n>=0 - Paolo P. Lava, Jul 08 2008

EXAMPLE

5*a(1)^2 + 7 = 5*10^2 + 7 = 507 = 3*13^2 = 3*A077246(1)^2.

CROSSREFS

Sequence in context: A081905 A016138 A006329 * A036732 A251309 A206764

Adjacent sequences:  A077242 A077243 A077244 * A077246 A077247 A077248

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Nov 08 2002

STATUS

approved

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Last modified November 18 12:21 EST 2017. Contains 294891 sequences.