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A316275
Lucas analog to A101361.
2
2, 3, 3, 7, 18, 123, 2207, 271443, 599074578, 162614600673847, 97418273275323406890123, 15841633607002416873831447357889638603, 1543264591854508694059691789796980188767738307671225999544322
OFFSET
0,1
COMMENTS
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.
LINKS
René Gy, Sequence in which adding 2 produces a square, Math StackExchange.
FORMULA
a(n) = A000032(2*A000045(n)) = Lucas(2*Fibonacci(n)).
MATHEMATICA
Table[LucasL[2 Fibonacci[n]], {n, 0, 10}]
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 *)
PROG
(PARI) a(n)={my(t=2*fibonacci(n)); fibonacci(t + 1) + fibonacci(t - 1)} \\ Andrew Howroyd, Mar 01 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
René Gy, Nov 23 2018
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, Mar 01 2020
STATUS
approved