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

0,2

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

Links

Table of n, a(n) for n=0..26.

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (0,8,0,-1).

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)

Example

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

Mathematica

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

Crossrefs

Cf. A077243, A077245, A077248.

Sequence in context: A127492 A258974 A366508 * A341032 A082939 A074069

Adjacent sequences: A077244 A077245 A077246 * A077248 A077249 A077250

Keyword

nonn,easy

Author

Wolfdieter Lang, Nov 08 2002

Status

approved