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A077244 Bisection (odd part) of Chebyshev sequence with Diophantine property. 5
3, 22, 173, 1362, 10723, 84422, 664653, 5232802, 41197763, 324349302, 2553596653, 20104423922, 158281794723, 1246149933862, 9810917676173, 77241191475522, 608118614128003, 4787707721548502, 37693543158260013, 296760637544531602, 2336391557197992803 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

3*a(n)^2 - 5*b(n)^2 = 7, with the companion sequence b(n)= A077243(n).

The even part is A077246(n) with Diophantine companion A077245(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 (8,-1).

FORMULA

a(n)= (2*T(n+1, 4)+T(n, 4))/3, with T(n, x) Chebyshev's polynomials of the first kind, A053120. T(n, 4)= A001091(n).

G.f.: (3-2*x)/(1-8*x+x^2).

From Colin Barker, Oct 12 2015: (Start)

a(n) = (((4-sqrt(15))^n * (-10+3*sqrt(15)) + (4+sqrt(15))^n * (10+3*sqrt(15)))) / (2*sqrt(15)).

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

(End)

EXAMPLE

22 = a(1) = sqrt((5*A077243(1)^2 + 7)/3) = sqrt((5*17^2 + 7)/3) = sqrt(484) = 22.

MATHEMATICA

LinearRecurrence[{8, -1}, {3, 22}, 25] (* Vincenzo Librandi, Oct 12 2015 *)

PROG

(PARI) Vec((3-2*x)/(1-8*x+x^2) + O(x^40)) \\ Colin Barker, Oct 12 2015

(MAGMA) I:=[3, 22]; [n le 2 select I[n] else 8*Self(n-1)-Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 12 2015

CROSSREFS

Sequence in context: A074578 A290719 A074576 * A138899 A147855 A278333

Adjacent sequences:  A077241 A077242 A077243 * A077245 A077246 A077247

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Nov 08 2002

STATUS

approved

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Last modified November 20 08:12 EST 2017. Contains 294962 sequences.