A077250 Bisection (odd part) of Chebyshev sequence with Diophantine property.

11, 103, 1019, 10087, 99851, 988423, 9784379, 96855367, 958769291, 9490837543, 93949606139, 930005223847, 9206102632331, 91131021099463, 902104108362299, 8929910062523527, 88396996516872971, 875040055106206183, 8662003554545188859, 85744995490345682407

Offset

0,1

Comments

a(n)^2 - 24*b(n)^2 = 25, with the companion sequence b(n) = A077249(n).

The even part is A077409(n) with Diophantine companion A077251(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 (10,-1).

Formula

a(n) = 10*a(n-1)- a(n-2), a(-1)=7, a(0)=11.

a(n) = 2*T(n+1, 5)+T(n, 5), with T(n, x) Chebyshev's polynomials of the first kind, A053120. T(n, 5)= A001079(n).

a(n) = sqrt(25 + 24*A077249(n)^2).

G.f.: (11-7*x)/(1-10*x+x^2).

Example

103 = a(1) = sqrt(24*A077249(1)^2 + 25) = sqrt(24*21^2 + 25) = sqrt(10609) = 103.

Mathematica

CoefficientList[Series[(11 - 7 z)/(z^2 - 10 z + 1), {z, 0, 200}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *)

Prog

(PARI) a(n)= 2*polchebyshev(n+1, 1, 5)+polchebyshev(n, 1, 5) \\ Charles R Greathouse IV, Jun 11 2011
(PARI) Vec((11-7*x)/(1-10*x+x^2) + O(x^30)) \\ Colin Barker, Jun 15 2015

Crossrefs

Sequence in context: A016133 A287833 A155594 * A356128 A173851 A358340

Adjacent sequences: A077247 A077248 A077249 * A077251 A077252 A077253

Keyword

nonn,easy

Author

Wolfdieter Lang, Nov 08 2002

Status

approved