A077235 Bisection (odd part) of Chebyshev sequence with Diophantine property.

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

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

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