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A111946 Triangle read by rows: T(n,k) = gcd(Fibonacci(n), Fibonacci(k)), 1 <= k <= n.

%I A111946 #31 Jan 05 2025 19:51:38
%S A111946 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,
%T A111946 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,
%U A111946 1,1,2,3,1,8,1,3,2,1,1,144,1,1,1,1,1,1,1
%N A111946 Triangle read by rows: T(n,k) = gcd(Fibonacci(n), Fibonacci(k)), 1 <= k <= n.
%C A111946 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.
%H A111946 T. D. Noe, <a href="/A111946/b111946.txt">Rows n = 1..150 of triangle, flattened</a>
%H A111946 P. Ribenboim, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/43-1/paper43-1-1.pdf">FFF (Favorite Fibonacci Flowers)</a>, Fib. Q. 43 (No. 1, 2005), 3-14.
%F A111946 T(n, k) = Fibonacci(gcd(n, k)).
%F A111946 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
%e A111946 Triangle begins:
%e A111946   1;
%e A111946   1, 1;
%e A111946   1, 1, 2;
%e A111946   1, 1, 1, 3;
%e A111946   1, 1, 1, 1, 5;
%e A111946   1, 1, 2, 1, 1, 8;
%e A111946   1, 1, 1, 1, 1, 1, 13;
%e A111946   1, 1, 1, 3, 1, 1,  1, 21;
%e A111946   1, 1, 2, 1, 1, 2,  1,  1, 34;
%e A111946   1, 1, 1, 1, 5, 1,  1,  1,  1, 55;
%e A111946   ...
%t A111946 T[ n_, k_] := Fibonacci @ GCD[ n, k] (* _Michael Somos_, Jul 18 2011 *)
%o A111946 (PARI) {T(n, k) = fibonacci( gcd( n, k))} /* _Michael Somos_, Jul 18 2011 */
%o A111946 (Magma) /* As triangle */ [[Gcd(Fibonacci(n), Fibonacci(k)): k in [1..n]]: n in [1.. 15]]; // _Vincenzo Librandi_, Dec 20 2015
%Y A111946 Cf. A000045, A111956, A111957.
%K A111946 nonn,tabl
%O A111946 1,6
%A A111946 _N. J. A. Sloane_, Nov 28 2005