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A111957
Triangle read by rows: T(n,k) = gcd(Fibonacci(n), Lucas(k)), 1 <= k <= n.
3
1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 7, 1, 3, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 4, 1, 1, 18, 1, 1, 4, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 29, 1, 1, 1, 1, 1, 1
OFFSET
1,6
LINKS
Paulo Ribenboim, FFF (Favorite Fibonacci Flowers), Fib. Quart. 43 (No. 1, 2005), 3-14.
FORMULA
T(n, k) = Lucas(g), where g = gcd(n, k), if n/g is even; = 2 if n/g is odd and 3|g; = 1 otherwise.
EXAMPLE
Triangle begins:
1,
1, 1,
1, 1, 2,
1, 3, 1, 1,
1, 1, 1, 1, 1,
1, 1, 4, 1, 1, 2,
1, 1, 1, 1, 1, 1, 1,
1, 3, 1, 7, 1, 3, 1, 1,
1, 1, 2, 1, 1, 2, 1, 1, 2,
1, 1, 1, 1, 11, 1, 1, 1, 1, 1,
=============================
MATHEMATICA
Flatten[Table[GCD[Fibonacci[n], LucasL[k]], {n, 20}, {k, n}]] (* Alonso del Arte, Dec 19 2015 *)
PROG
(Magma) /* As triangle */ [[Gcd(Fibonacci(n), Lucas(k)): k in [1..n]]: n in [1.. 15]]; // Vincenzo Librandi, Dec 20 2015
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Nov 28 2005
STATUS
approved