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%I #46 Mar 28 2020 15:12:07
%S 2,3,3,7,18,123,2207,271443,599074578,162614600673847,
%T 97418273275323406890123,15841633607002416873831447357889638603,
%U 1543264591854508694059691789796980188767738307671225999544322
%N Lucas analog to A101361.
%C This is the sequence defined by the third-order non-linear recurrence a(n+1) = a(n)*a(n-1) - a(n-2) and a(0)=2, a(1)=3, a(2)=3.
%H Andrew Howroyd, <a href="/A316275/b316275.txt">Table of n, a(n) for n = 0..17</a>
%H René Gy, <a href="https://math.stackexchange.com/a/3007124/130022">Sequence in which adding 2 produces a square</a>, Math StackExchange.
%F a(n) = A000032(2*A000045(n)) = Lucas(2*Fibonacci(n)).
%t Table[LucasL[2 Fibonacci[n]], {n, 0, 10}]
%t RecurrenceTable[{a[0]==2,a[1]==a[2]==3,a[n+1]==a[n]a[n-1]-a[n-2]},a,{n,20}] (* _Harvey P. Dale_, Mar 28 2020 *)
%o (PARI) a(n)={my(t=2*fibonacci(n)); fibonacci(t + 1) + fibonacci(t - 1)} \\ _Andrew Howroyd_, Mar 01 2020
%Y Cf. A000032, A000045, A101361.
%K nonn
%O 0,1
%A _René Gy_, Nov 23 2018
%E Terms a(11) and beyond from _Andrew Howroyd_, Mar 01 2020
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