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

Author

Wolfdieter Lang, Nov 08 2002

Keywords

• nonn
• easy

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).

Examples

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

Links

• Tanya Khovanova, Recursive Sequences
• Index entries for sequences related to Chebyshev polynomials.
• Index entries for linear recurrences with constant coefficients, signature (8,-1).

Programs

Mathematica

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

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).