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%I #19 Sep 08 2022 08:45:21
%S 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,
%T 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,
%U 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
%N Triangle read by rows: T(n,k) = gcd(Fibonacci(n), Lucas(k)), 1 <= k <= n.
%H G. C. Greubel, <a href="/A111957/b111957.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%H Paulo Ribenboim, <a href="http://www.fq.math.ca/Papers1/43-1/paper43-1-1.pdf">FFF (Favorite Fibonacci Flowers)</a>, Fib. Quart. 43 (No. 1, 2005), 3-14.
%F 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.
%e Triangle begins:
%e 1,
%e 1, 1,
%e 1, 1, 2,
%e 1, 3, 1, 1,
%e 1, 1, 1, 1, 1,
%e 1, 1, 4, 1, 1, 2,
%e 1, 1, 1, 1, 1, 1, 1,
%e 1, 3, 1, 7, 1, 3, 1, 1,
%e 1, 1, 2, 1, 1, 2, 1, 1, 2,
%e 1, 1, 1, 1, 11, 1, 1, 1, 1, 1,
%e =============================
%t Flatten[Table[GCD[Fibonacci[n], LucasL[k]], {n, 20}, {k, n}]] (* _Alonso del Arte_, Dec 19 2015 *)
%o (Magma) /* As triangle */ [[Gcd(Fibonacci(n), Lucas(k)): k in [1..n]]: n in [1.. 15]]; // _Vincenzo Librandi_, Dec 20 2015
%Y Cf. A000045, A000032, A111946, A111956.
%K nonn,tabl
%O 1,6
%A _N. J. A. Sloane_, Nov 28 2005
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