A316275 Lucas analog to A101361.

2, 3, 3, 7, 18, 123, 2207, 271443, 599074578, 162614600673847, 97418273275323406890123, 15841633607002416873831447357889638603, 1543264591854508694059691789796980188767738307671225999544322

Offset: 0

Author

René Gy, Nov 23 2018

Keywords

• nonn

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

• Andrew Howroyd, Table of n, a(n) for n = 0..17
• René Gy, Sequence in which adding 2 produces a square, Math StackExchange.

Crossrefs

Cf. A000032, A000045, A101361.

Programs

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 *)

PARI

a(n)={my(t=2*fibonacci(n)); fibonacci(t + 1) + fibonacci(t - 1)} \\ Andrew Howroyd, Mar 01 2020

Formula

a(n) = A000032(2*A000045(n)) = Lucas(2*Fibonacci(n)).

Extensions

Terms a(11) and beyond from Andrew Howroyd, Mar 01 2020