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%I #14 Sep 08 2022 08:45:07
%S 1,2,12,21,119,208,1178,2059,11661,20382,115432,201761,1142659,
%T 1997228,11311158,19770519,111968921,195707962,1108378052,1937309101,
%U 10971811599,19177383048,108609737938
%N Combined Diophantine Chebyshev sequences A077249 and A077251.
%C -24*a(n)^2 + b(n)^2 = 25, with the companion sequence b(n)= A077411(n).
%H G. C. Greubel, <a href="/A077410/b077410.txt">Table of n, a(n) for n = 0..1000</a>
%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 (0,10,0,-1).
%F a(2*k) = A077251(k) and a(2*k+1) = A077249(k), k>=0.
%F a(n) = sqrt((A077411(n)^2 - 25)/24).
%F G.f.: (1+x)*(1+x+x^2)/(1-10*x^2+x^4).
%e 24*a(2)^2 + 25 = 24*12^2 + 25 = 3481 = 59^2 = A077411(2)^2.
%t CoefficientList[Series[(1+x)*(1+x+x^2)/(1-10*x^2+x^4), {x,0,50}], x] (* or *) LinearRecurrence[{0,10,0,-1}, {1,2,12,21}, 30] (* _G. C. Greubel_, Jan 18 2018 *)
%o (PARI) x='x+O('x^30); Vec((1+x)*(1+x+x^2)/(1-10*x^2+x^4)) \\ _G. C. Greubel_, Jan 18 2018
%o (Magma) I:=[1,2,12,21]; [n le 4 select I[n] else 10*Self(n-2) - Self(n-4): n in [1..30]]; // _G. C. Greubel_, Jan 18 2018
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Nov 08 2002
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