A077247 - OEIS

%I #16 Nov 12 2022 16:07:51

%S 1,2,10,17,79,134,622,1055,4897,8306,38554,65393,303535,514838,

%T 2389726,4053311,18814273,31911650,148124458,251239889,1166181391,

%U 1978007462,9181326670,15572819807,72284431969,122604550994,569094129082

%N Combined Diophantine Chebyshev sequences A077245 and A077243.

%C -5*a(n)^2 + 3*b(n)^2 = 7, with the companion sequence b(n)= A077248(n).

%C 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

%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,8,0,-1).

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

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

%F From _Klaus Purath_, Aug 12 2021: (Start)

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

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

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

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

%t LinearRecurrence[{0,8,0,-1},{1,2,10,17},30] (* _Harvey P. Dale_, Nov 12 2022 *)

%Y Cf. A077243, A077245, A077248.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Nov 08 2002