A097351 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

Offset

1,2

Comments

In every row, the limiting ratio of consecutive terms is tau.

Links

Table of n, a(n) for n=1..80.

Formula

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.

Example

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

Crossrefs

Cf. A000045, A097352.

Sequence in context: A142249 A274705 A257243 * A207330 A048600 A100578

Adjacent sequences: A097348 A097349 A097350 * A097352 A097353 A097354

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 08 2004

Status

approved