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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
Tanya Khovanova, Recursive Sequences
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
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
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Nov 08 2002
STATUS
approved

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Last modified April 16 23:37 EDT 2024. Contains 371756 sequences. (Running on oeis4.)