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_Clark Kimberling (ck6(AT)evansville.edu), _, Aug 08 2004
Rectangular array T(n,k) by antidiagonals; rows are generalized Fibonacci sequences, and every relatively prime pair (i,j) satisfying 1 <= i < j occurs exactly once.
nonn,tabl,new
Recurrence for row n: T(n, k)=T(n, k-1)+T(n, k-2). Each row after the first begins with lexically least relatively prime pair not in previous rows.
nonn,tabl,new
Rectangular array T(n,k) by antidiagonals; rows are generalized Fibonacci sequences, and every relatively prime pair (i,j) satisfying 1 <= i < j occurs exactly once.
1, 2, 1, 3, 3, 1, 5, 4, 4, 1, 8, 7, 5, 5, 1, 13, 11, 9, 6, 6, 2, 21, 18, 14, 11, 7, 5, 1, 34, 29, 23, 17, 13, 7, 7, 1, 55, 47, 37, 28, 20, 12, 8, 8, 2, 89, 76, 60, 45, 33, 19, 15, 9, 7, 1, 144, 123, 97, 73, 53, 31, 23, 17, 9, 9, 3, 233, 199, 157, 118, 86, 50, 38, 26, 16, 10, 7, 1, 377, 322
1,2
In every row, the limiting ratio of consecutive terms is tau.
Recurrence for row n: T(n,k)=T(n,k-1)+T(n,k-2). Each row after the first begins with lexically least relatively prime pair not in previous rows.
Northwest corner:
1 2 3 5 8
1 3 4 7 11
1 4 5 9 14
1 5 6 11 17
1 6 7 13 20
2 5 7 12 19
nonn,tabl
Clark Kimberling (ck6(AT)evansville.edu), Aug 08 2004
approved