A077247 Combined Diophantine Chebyshev sequences A077245 and A077243.

1, 2, 10, 17, 79, 134, 622, 1055, 4897, 8306, 38554, 65393, 303535, 514838, 2389726, 4053311, 18814273, 31911650, 148124458, 251239889, 1166181391, 1978007462, 9181326670, 15572819807, 72284431969, 122604550994, 569094129082

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)= A077248(n).

In addition to the comment above: 3*b(n)^2 = 5*a(n-2)*a(n+2) + 112, where b(n) = (a(n+2) - a(n-2))/6 = A077248(n), n >= 2. - Klaus Purath, Aug 12 2021

Examples

			5*a(1)^2 + 7 = 5*4 + 7 = 27 = 3*3^2 = 3*A077248(1)^2.
		

Links

• Index entries for sequences related to Chebyshev polynomials.
• Index entries for linear recurrences with constant coefficients, signature (0,8,0,-1).

Crossrefs

Cf. A077243, A077245, A077248.

Programs

Mathematica

LinearRecurrence[{0,8,0,-1},{1,2,10,17},30] (* Harvey P. Dale, Nov 12 2022 *)

Formula

a(2*k)= A077245(k) and a(2*k+1)= A077243(k), k>=0.

G.f.: (1+x)*(1+x+x^2)/(1-8*x^2+x^4).

From Klaus Purath, Aug 12 2021: (Start)

a(n) = 8*a(n-2) - a(n-4), n >= 4.

a(n) = (a(n-2)*a(n-4) - 168)/a(n-6), n >= 6.

a(n) = (a(n-1)*a(n-2) - 15/2 - 9/2*(-1)^n)/a(n-3), n >= 3. (End)