A111956 Triangle read by rows: T(n,k) = gcd(Lucas(n), Lucas(k)), 1 <= k <= n.

1, 1, 3, 1, 1, 4, 1, 1, 1, 7, 1, 1, 1, 1, 11, 1, 3, 2, 1, 1, 18, 1, 1, 1, 1, 1, 1, 29, 1, 1, 1, 1, 1, 1, 1, 47, 1, 1, 4, 1, 1, 2, 1, 1, 76, 1, 3, 1, 1, 1, 3, 1, 1, 1, 123, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 199, 1, 1, 2, 7, 1, 2, 1, 1, 2, 1, 1, 322, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 521

Offset: 1

Author

N. J. A. Sloane, Nov 28 2005

Keywords

• nonn
• tabl

Links

• Harvey P. Dale, Rows n = 1..141 of triangle, flattened
• Paulo Ribenboim, FFF (Favorite Fibonacci Flowers), Fib. Quart. 43 (No. 1, 2005), 3-14.

Crossrefs

Cf. A000032, A111946, A111957.

Programs

Mathematica

Flatten[Table[GCD[LucasL[n], LucasL[k]], {n,20}, {k,n}]] (* Harvey P. Dale, Nov 23 2012 *)

PARI

for(n=1,10, for(k=1,n, print1(gcd(fibonacci(n+1) + fibonacci(n-1), fibonacci(k+1) + fibonacci(k-1)), ", "))) \\ G. C. Greubel, Dec 17 2017

Formula

T(n, k) = Lucas(g), where g = gcd(n, k), if n/g and k/g are odd; = 2 if n/g or k/g are even and 3|g; = 1 otherwise.