A077247 - OEIS

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

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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