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A111946
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Triangle read by rows: T(n,k) = gcd(Fibonacci(n), Fibonacci(k)), 1 <= k <= n.
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3
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1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 5, 1, 1, 2, 1, 1, 8, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 3, 1, 1, 1, 21, 1, 1, 2, 1, 1, 2, 1, 1, 34, 1, 1, 1, 1, 5, 1, 1, 1, 1, 55, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 89, 1, 1, 2, 3, 1, 8, 1, 3, 2, 1, 1, 144, 1, 1, 1, 1, 1, 1, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,6
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COMMENTS
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The function T(n, k) is defined for all integers n, k but only the values for 1 <= k <= n as a triangular array are listed here.
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LINKS
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FORMULA
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T(n, k) = Fibonacci(gcd(n, k)).
T(n, k) = T(k, n) = T(-n, k) = T(n, -k) = T(n, n+k) = T(n+k, k). - Michael Somos, Jul 18 2011
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EXAMPLE
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Triangle begins:
1;
1, 1;
1, 1, 2;
1, 1, 1, 3;
1, 1, 1, 1, 5;
1, 1, 2, 1, 1, 8;
1, 1, 1, 1, 1, 1, 13;
1, 1, 1, 3, 1, 1, 1, 21;
1, 1, 2, 1, 1, 2, 1, 1, 34;
1, 1, 1, 1, 5, 1, 1, 1, 1, 55;
...
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MATHEMATICA
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T[ n_, k_] := Fibonacci @ GCD[ n, k] (* Michael Somos, Jul 18 2011 *)
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PROG
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(PARI) {T(n, k) = fibonacci( gcd( n, k))} /* Michael Somos, Jul 18 2011 */
(Magma) /* As triangle */ [[Gcd(Fibonacci(n), Fibonacci(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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