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A111957
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Triangle read by rows: T(n,k) = gcd(Fibonacci(n), Lucas(k)), 1 <= k <= n.
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3
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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
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OFFSET
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1,6
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LINKS
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FORMULA
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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.
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EXAMPLE
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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,
=============================
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MATHEMATICA
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Flatten[Table[GCD[Fibonacci[n], LucasL[k]], {n, 20}, {k, n}]] (* Alonso del Arte, Dec 19 2015 *)
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PROG
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(Magma) /* As triangle */ [[Gcd(Fibonacci(n), Lucas(k)): k in [1..n]]: n in [1.. 15]]; // Vincenzo Librandi, Dec 20 2015
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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