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A077235 Bisection (odd part) of Chebyshev sequence with Diophantine property. 6
5, 16, 59, 220, 821, 3064, 11435, 42676, 159269, 594400, 2218331, 8278924, 30897365, 115310536, 430344779, 1606068580, 5993929541, 22369649584, 83484668795, 311569025596, 1162791433589, 4339596708760, 16195595401451, 60442784897044, 225575544186725 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n)^2 - 3*b(n)^2 = 13, with the companion sequence b(n) = A077234(n).

The even part is A077236(n) with Diophantine companion A054491(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 (4,-1)

FORMULA

a(n) = 2*T(n+1, 2)+T(n, 2), with T(n, x) Chebyshev's polynomials of the first kind, A053120. T(n, 2)= A001075(n).

G.f.: (5-4*x)/(1-4*x+x^2).

a(n) = 4*a(n-1)-a(n-2) with a(0)=5 and a(1)=16. - Philippe Deléham, Nov 16 2008

a(n) = -sqrt(3)*[2-sqrt(3)]^n+sqrt(3)*[2+sqrt(3)]^n+(5/2)*[2-sqrt(3)]^n+(5/2)*[2+sqrt(3)]^n, with n>=0. - Paolo P. Lava, Nov 20 2008

EXAMPLE

16 = a(1) = sqrt(3*A077234(1)^2 + 13) = sqrt(3*9^2 + 13)= sqrt(256) = 16.

PROG

(PARI) Vec((5-4*x)/(1-4*x+x^2) + O(x^100)) \\ Colin Barker, Jun 16 2015

CROSSREFS

Cf. A077238 (even and odd parts).

Sequence in context: A116914 A047103 A226897 * A203232 A098347 A203414

Adjacent sequences:  A077232 A077233 A077234 * A077236 A077237 A077238

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Nov 08 2002

STATUS

approved

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Last modified September 22 19:04 EDT 2018. Contains 315270 sequences. (Running on oeis4.)