A077245 Bisection (even part) of Chebyshev sequence with Diophantine property.

1, 10, 79, 622, 4897, 38554, 303535, 2389726, 18814273, 148124458, 1166181391, 9181326670, 72284431969, 569094129082, 4480468600687, 35274654676414, 277716768810625, 2186459495808586, 17213959197658063

Offset: 0

Author

Wolfdieter Lang, Nov 08 2002

Keywords

• nonn
• easy

Comments

3*b(n)^2 - 5*a(n)^2 = 7, with the companion sequence b(n)= A077246(n).

The odd part is A077243(n) with Diophantine companion A077244(n).

Examples

			5*a(1)^2 + 7 = 5*10^2 + 7 = 507 = 3*13^2 = 3*A077246(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).

Formula

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

a(n)= S(n, 8)+2*S(n-1, 8), with S(n, x) := U(n, x/2), Chebyshev's polynomials of the 2nd kind, A049310. S(-1, x) := 0 and S(n, 8)= A001090(n+1).

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