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A077250 Bisection (odd part) of Chebyshev sequence with diophantine property. +0
5
11, 103, 1019, 10087, 99851, 988423, 9784379, 96855367, 958769291, 9490837543, 93949606139, 930005223847, 9206102632331, 91131021099463, 902104108362299, 8929910062523527, 88396996516872971, 875040055106206183 (list; graph; listen)
OFFSET

0,1

COMMENT

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

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

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.

CROSSREFS

Adjacent sequences: A077247 A077248 A077249 this_sequence A077251 A077252 A077253

Sequence in context: A081552 A141915 A016133 this_sequence A099839 A075183 A116011

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 08 2002

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Last modified October 11 09:12 EDT 2008. Contains 144832 sequences.


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