A111957 Triangle read by rows: T(n,k) = gcd(Fibonacci(n), Lucas(k)), 1 <= k <= n.

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

Author

N. J. A. Sloane, Nov 28 2005

Keywords

• nonn
• tabl

Examples

			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,
=============================
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
• Paulo Ribenboim, FFF (Favorite Fibonacci Flowers), Fib. Quart. 43 (No. 1, 2005), 3-14.

Crossrefs

Cf. A000045, A000032, A111946, A111956.

Programs

Magma

/* As triangle */ [[Gcd(Fibonacci(n), Lucas(k)): k in [1..n]]: n in [1.. 15]]; // Vincenzo Librandi, Dec 20 2015

Mathematica

Flatten[Table[GCD[Fibonacci[n], LucasL[k]], {n, 20}, {k, n}]] (* Alonso del Arte, Dec 19 2015 *)

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.