A077243 Bisection (odd part) of Chebyshev sequence with Diophantine property.

2, 17, 134, 1055, 8306, 65393, 514838, 4053311, 31911650, 251239889, 1978007462, 15572819807, 122604550994, 965263588145, 7599504154166, 59830769645183, 471046653007298, 3708542454413201, 29197292982298310

Offset

0,1

Comments

-5*a(n)^2 + 3* b(n)^2 = 7, with the companion sequence b(n)= A077244(n).

The even part is A077245(n) with Diophantine companion A077246(n).

Links

Table of n, a(n) for n=0..18.

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (8,-1).

Formula

a(n)= 8*a(n-1) - a(n-2), a(-1)=-1, a(0)=2.

a(n)= 2*S(n, 8)+S(n-1, 8), with S(n, x) := U(n, x/2), Chebyshev polynomials of 2nd kind, A049310. S(n, 8)= A001090(n+1).

G.f.: (2+x)/(1-8*x+x^2).

Example

5*a(1)^2 + 7 = 5*17^2+7 = 1452 = 3*22^2 = 3*A077244(1)^2.

Mathematica

LinearRecurrence[{8, -1}, {2, 17}, 30] (* Harvey P. Dale, Oct 03 2015 *)

Crossrefs

Sequence in context: A007354 A180840 A261120 * A037525 A037734 A201782

Adjacent sequences: A077240 A077241 A077242 * A077244 A077245 A077246

Keyword

nonn,easy

Author

Wolfdieter Lang, Nov 08 2002

Status

approved