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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,6

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.

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

Cf. A000045, A000032, A111946, A111956.

Sequence in context: A144966 A320000 A119805 * A125168 A324725 A328392

Adjacent sequences:  A111954 A111955 A111956 * A111958 A111959 A111960

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Nov 28 2005

STATUS

approved

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Last modified February 19 13:23 EST 2020. Contains 332044 sequences. (Running on oeis4.)