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

0,2

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).

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) := -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).

Example

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

Crossrefs

Sequence in context: A081905 A016138 A006329 * A036732 A251309 A377348

Adjacent sequences: A077242 A077243 A077244 * A077246 A077247 A077248

Keyword

nonn,easy

Author

Wolfdieter Lang, Nov 08 2002

Status

approved