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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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2
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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, 1, 1, 1, 1, 1, 233, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| 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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REFERENCES
| P. Ribenboim, FFF (Favorite Fibonacci Flowers), Fib. Q. 43 (No. 1, 2005), 3-14.
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FORMULA
| 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
| {1}; {1,1}; {1,1,2}; {1,1,1,3}; {1,1,1,1,5}; {1,1,2,1,1,8}; ...
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MATHEMATICA
| T[ n_, k_] := Fibonacci @ GCD[ n, k] (* Michael Somos, Jul 18 2011 *)
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PROG
| (PARI) {T(n, k) = fibonacci( gcd( n, k))} /* Michael Somos, Jul 18 2011 */
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CROSSREFS
| Cf. A000045, A111956, A111957.
Sequence in context: A085476 A124944 A094392 * A175788 A137844 A079229
Adjacent sequences: A111943 A111944 A111945 * A111947 A111948 A111949
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KEYWORD
| nonn,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 28 2005
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