A111946 -id:A111946 - cp's OEIS frontend

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

N. J. A. Sloane, Nov 28 2005

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

Cf. A000032, A111946, A111957.

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

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

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.

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

Original entry on oeis.org

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

N. J. A. Sloane, Nov 28 2005

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

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.

Cf. A000045, A000032, A111946, A111956.

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

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

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.

cp's OEIS Frontend

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

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